Ali Jameel

Sohar University · Faculty of Education and Arts

This work focuses on finding closed-form analytic solutions of a higher-dimensional fractional model, in conformable sense, known by the (4+1)-dimensional Fokas equation. Fractional partial differential equations (FPDEs) and systems can describe heritable real-world occurrences. However, solving such models can be difficult, especially for nonlinea...

في هذا العمل، يؤدي التحقيق في عدد قليل من التبعية التفاضلية بالإضافة إلى التنسيق الفائق إلى تضمين فئة محددة مذكورة في مجال الدوال الميرومورفية أحادية التكافؤ داخل قرص وحدة مفتوحة مثقوبة. واستخلاص بعض نظريات الساندويتش. الغرض من هذه المقالة هو النظر في عدد قليل من خصائص التبعية المتغيرة للدوال التحليلية أحادية التكافؤ على قرص وحدة مثقوب. ويهدف بالإض...

In order to obtain sufficient solutions for fuzzy differential equations (FDEs), reliable and efficient approximation methods are necessary. Approximate numerical methods can not directly solve fuzzy HIV models. Meanwhile, the approximate analytical methods can potentially provide more straightforward solutions without the need for extensive numeri...

The fundamental purpose of this investigation is to make use of an analytical approach in order to solve and assess initial boundary value problems that are in the form of fractional partial differential equations (FPDEs). Intricate scientific phenomena that are marked by hereditary characteristics that are passed down from one generation to the ne...

Using Mathematica computer software, a numerical procedure called the modified Adomian decomposition method (MADM) is successfully implemented for obtaining exact solutions of some classes of Volterra integro-differential equations based on the ADM approximate series solutions, Laplace transform, and Pade approximants. The reliability and effective...

The variational iteration method is used to deal with linear and nonlinear differential equations. The main characteristics of the method lie in its flexibility and ability to accurately and easily solve nonlinear equations. In this work, a general framework is presented for a variational iteration method for the analytical treatment of partial dif...

The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approache...

Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that invo...

This study presents a novel computational methodology for resolving second-order fuzzy initial value problems (FIVPs), encompassing ordinary differential equations. The proposed approach modifies the conventional crisp fifth-order Runge-Kutta Fehlberg method to suit the resolution of second-order FIVPs within the fuzzy domain, drawing on concepts f...

There are various linear and nonlinear one-dimensional partial differential equations that are the focus of this research. There are a large number of these equations that cannot be solved analytically or precisely. The evaluation of nonlinear partial differential equations, even if analytical solutions exist, may be problematic. Therefore, it may...

This work focuses on solving and analyzing two-point fuzzy boundary value problems in the form of fractional ordinary differential equations (FFOBVPs) using a new version of the approximation analytical approach. FFOBVPs are useful in describing complex scientific phenomena that include heritable characteristics and uncertainty, and obtaining exact...

Rössler systems are introduced as prototype equations with the minimum ingredients for continuous time chaos. These systems are made up of three nonlinear ordinary differential equations that define a continuous-time dynamical system with chaotic dynamics due to the attractor's fractal features. Recently, the study on dynamics of fractional-order R...

Fractional differential equations with strong nonlinearity are important in modelling complex physical phenomena. Therefore, there is an urgent need to employ new technique to help researches and physicists to understand the physical problems better and to deal with such equations. In this paper, we develop and analyze a semi-analytical technique c...

The Homotopy Analysis Method (HAM) is an approximate-analytical method for solving linear and nonlinear problems. HAM provides the auxiliary or convergence parameter, which considered as a powerful tool to examine and analyze the precision of the approximate series solution and ensure its convergence. In this article, fuzzy set theory properties is...

This paper is devoted to study the existence and uniqueness of a solution for the following fractional hybrid differential equations defined by Riemann-Liouville differential operator order of 0 < α < 1 D α t 0 + x(t) − f 1 (t, x(t)) = f 2 t, x(t) , a.e t ∈ J, x(t 0) = x 0 ∈ R, (1.0) where D α t 0 + is the Riemann-Liouville fractional derivative or...

In this work, the fuzzy fractional two-point boundary value problems (FFTBVPs) are analyzed and solved using the fuzzy fractional homotopy analysis method (FF-HAM). Fuzzy set theory mixed with Caputo fractional derivative properties is utilized to produce a new formulation of the standard HAM in the fuzzy domain for the persistence of approximation...

it is common knowledge that partial differential equations are becoming increasingly relevant in modern research and that the solutions to these equations are essential for addressing a wide variety of real-world applications. The primary objective of this study is to investigate possible approximations for solving the nonlinear Kaup-Kupershmidt (K...

In this paper, a numerical scheme so-called modified differential transformation method (MDTM) based on differential transformation method (DTM), Laplace transform and Padé approximation will be used to obtain accurate approximate solution for a class of boundary value problems (BVP's). The MDTM is employed as an alternative technique to overcome s...

Partial differential equations are known to be increasingly important in today’s research, and their solutions are paramount for tackling numerous real-life applications. This article extended the analytical scheme of the homotopy analysis method (HAM) to develop an approximate analytical solution for Fuzzy Partial Differential Equations (FPDEs). T...

This paper devotes to constructing an approximate analytic solution for the hyperchaotic finance model. The model describes the time variation of the interest rate, the investment demand, the price exponent, and the average profit margin. The multistage homotopy analysis method (MHAM) and multistage variational iteration method (MVIM) are utilized...

In this work, the Optimal Homotopy Asymptotic Method (OHAM) is prolifically implemented to find the optimal solutions of fractional order of fuzzy differential equations. We inspect the competence of the method by examining fractional order time-dependent first order fuzzy initial value problems in the Caputo derivative sense. The concepts of fuzzy...

In this paper, a modified procedure based on the residual power series method (RPSM) was implemented to achieve approximate solution with high degree of accuracy for a system of multi-pantograph type delay differential equations (DDEs). This modified procedure is considered as a hybrid technique used to improve the curacy of the standard RPSM by co...

This paper aims to solve the nonlinear two-point fuzzy boundary value problem (TPFBVP) using approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be challenging to evaluate. Therefore, approximate analytical methods may be necessary to consider...

This paper investigates the powerful method namely the homotopy analysis method (HAM), to solve the fuzzy pantograph equation (FPE) in approximate analytic form. HAM yields a convergent infinite series solution to the solution of FPE without the need to reduce the FPE to the first order system or compare it with the exact solution, and this is one...

In this work the Homotopy perturbation method (HPM) has been implemented in order to provide approximate analytical solutions to linear initial value problems for HIV infection model. The HPM approach allows unknown parameters to be defined by a few iteration steps for the obtained series solution. The model describes the number of unknown immune c...

A warrant is a financial agreement that gives the right but not the responsibility, to buy or sell a security at a specific price prior to expiration. Many researchers inadvertently utilize call option pricing models to price equity warrants, such as the Black Scholes model which had been found to hold many shortcomings. This paper investigates the...

The Bezier curve is a parametric curve used in the graphics of a computer and related areas. This curve, connected to the polynomials of Bernstein, is named after the design curves of Renault's cars by Pierre Bézier in the 1960s. There has recently been considerable focus on finding reliable and more effective approximate methods for solving differ...

There has recently been considerable focus on finding reliable and more effective approximate methods for solving biological mathematical models in the form of differential equations. One of the well-known approximate or semi-analytical methods for solving linear, nonlinear differential well as partial differential equations within various fields o...

There has recently been considerable focus on finding reliable and more effective numerical methods for solving different mathematical problems with integral equations. The Runge-Kutta methods in numerical analysis are a family of iterative methods, both implicit and explicit, with different orders of accuracy, used in temporal and modification for...

Prior studies revealed that most researchers tend to employ the Black Scholes model to price equity warrants. However, the Black Scholes model was found deficient by contributing to large estimation errors and mispricing of equity warrants. Therefore, issues involving equity warrants are discussed in this paper, by focusing on specific topics and r...

Homotopy Analysis Method (HAM) is semi-analytic method to solve the linear and nonlinear mathematical models which can be used to obtain the approximate solution. The HAM includes an auxiliary parameter, which is an efficient way to examine and analyze the accuracy of linear and nonlinear problems. The main aim of this work is to explore the approx...

In this work, we developed an approximate analytical method based on the optimal homotopy asymptotic method (OHAM) to solve fuzzy partial differential equations (FPDE). The method has been applied to fuzzy reaction-diffusion equation with initial condition. By means of illustrative examples, we demonstrated the accuracy, efficiency, and flexibility...

The use of fuzzy partial differential equations has become an important tool in which uncertainty or vagueness exists to model real-life problems. In this article, two numerical techniques based on finite difference schemes that are the centered time center space and implicit schemes to solve fuzzy wave equations were used. The core of the article...

This article discusses an approximate scheme for solving one-dimensional heat-like and wave-like equations in fuzzy environment based on the homotopy perturbation method (HPM). The concept of topology in homotopy is used to create a convergent series solution of the fuzzy equations. The objective of the study is to formulate the double parametric f...

This research focuses on the approximate solutions of second-order fuzzy differential equations with fuzzy initial condition with two different methods depending on the properties of the fuzzy set theory. The methods in this research based on the Optimum homotopy asymptotic method (OHAM) and homotopy analysis method (HAM) are used implemented and a...

Delay differential equations (known as DDEs) are a broad use of many scientific researches and engineering applications. They come because the pace of the shift in their mathematical models relies all the basis not just on their present condition, but also on a certain past cases. In this work, we propose an algorithm of the approximate method to s...

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-u...

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-u...

In this article, we proposed an efficient method to solve the delay Fractional Bagley-Torvik equation. The proposed method is capable of reducing the volume of the computational work as compared to the classical techniques while still maintaining the high accuracy of the numerical result; the size reduction amounts to an improvement of the performa...

The purpose of this analysis would be to provide a computational technique for the numerical solution of second-order nonlinear fuzzy initial value (FIVPs). The idea is based on the reformulation of the fifth order Runge Kutta with six stages (RK56) from crisp domain to the fuzzy domain by using the definitions and properties of fuzzy set theory to...

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear...

Previous studies revealed that most local researchers frequently used the Black Scholes model to price equity warrants. However, the Black Scholes model was perceived of possessing too many drawbacks, such as big errors of estimation and mispricing of equity warrants. In this work, we consider the problem of pricing hybrid equity warrants based on...

Delay differential equations (known as DDEs) are a broad use of many scientific researches and engineering applications. They come because the pace of the shift in their mathematical models relies all the basis not just on their present condition, but also on a certain past cases. In this work, we propose an algorithm of the approximate metho...

To solve fuzzy partial differential equations (FPDE), we develop an approximate analytical method which is based on Optimal Homotopy Asymptotic Method (OHAM). The method with a Single convergent control parameter has been applied to Fuzzy Heat Equation (FHE) with fuzzy initial condition. An illustrative example has been given to demonstrate the acc...

In this paper, an approximate analytical solution for solving the fuzzy Bratu equation based on variation iteration method (VIM) is analyzed and modified without needed of any discretization by taking the benefits of fuzzy set theory. VIM is applied directly, without being reduced to a first order system, to obtain an approximate solution of the un...

The main objective of this paper is to obtain a new accurate approximate solutions for a kind of ordinary differential equations called multipoint boundary value problems by using simple modification of optimal homotopy asymptotic method (OHAM). This procedure is a well-performance for calculating a better approximate solutions using one-order of ap...

In this paper, we consider the numerical solution of the vorticity transport equation (V.T.E.), which is the basic non-dimensional nonlinear parabolic partial differential equation that governs unsteady flow problem, in two dimensions. We study the alternative direction implicit (A.D.I.) finite difference formula, which can be used to compute the n...

In this research, we investigate the numerical solution for the general class of first order Volterra integro- differential equation (VIDE). A scheme based on second, fourth and sixth order Runge-Kutta methods for ordinary differential equation is modified and analyzed to obtain a numerical solution for our proposed problem. We implement and compar...

In this paper the Homotopy Perturbation Method (HPM) is employed to solve n’thorder (n ≥ 2) non linear two point fuzzy boundary value problems (TPFBVP). The homotopy perturbation method can be used for solving n’th order fuzzy differential equations directly without reduction to first order system. The convergence theorem of this method in fuzzy case...

In this paper, an approximate analytical algorithm namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of first order fuzzy delay differential equations (FDDEs). This method allows for the solution of the FDDEs to be calculated in the form of an infinite series with the components that ca...

This study discusses the approximate solution of nonlinear Volterra Hammerstein Integral Equations (VHIEs) using Homotopy Perturbation Method (HPM). Based on the previous literature, the use of HPM for solving VHIEs are very limited. Most of them focus toward the solving of Fredholm and Volterra integro-differential equations. In this proposed meth...

The point of this paper is to present and analyze a numerical method to illuminate fuzzy initial value problems (FIVPs) including nonlinear fuzzy differential equations. The primary thought is based reformulate the six stages Runge Kutta strategy of order five (RK65) from crisp case to fuzzy case by taking the advantage of fuzzy set theory properti...

This work employs the Homotopy Perturbation Method (HPM) to develop an approximate analytical solution for a Fuzzy Partial Differential Equations (FPDE). The method is applied to calculate the solution of fuzzy reaction-diffusion equation (FRDE) by using the properties of fuzzy set theory. Examples are given to verify results compared with the exac...

The objective of this paper is to obtain an approximate solution to a singularly flustered boundary worth issues involving differential equation using differential construction technique. The specific procedure of the weight coefficients for estimation of derivatives are obtained by means of g-spline interpolation method. An illustrative example ha...

In this study, the fractional order of tumor cell growth and their interactions with effectors such as cytotoxic T-cells, E1(t) and natural killer cells E2(t) are studied. The Adam-Bashforth-Moulton algorithm is used 1 2 to numerically solve and simulate the model of the tumor immune system with fractional order. From the observation of the numeric...

In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an inf...

In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an inf...

In this study, the fractional order of tumor cell growth and their interactions with effectors such as cytotoxic T-cells, E1(t) and natural killer cells E2(t) are studied. The Adam-Bashforth-Moulton algorithm is used 1 2 to numerically solve and simulate the model of the tumor immune system with fractional order. From the observation of the numeric...

In this paper, a numerical procedure called multistage optimal homotopy asymptotic method (MOHAM) is introduced to solve multi-pantograph equations with time delay. It was shown that the MOHAM algorithm rapidly provides accurate convergent approximate solutions of the exact solution using only one term. A comparative study between the proposed meth...

In this paper, we discuss the numerical solution of second-order nonlinear two-point fuzzy boundary value problems (TPFBVP) by combining the finite difference method with Newton’s method. Numerical example using the well-known nonlinear TPFBVP is presented to show the capability of the new method in this regard and the results are satisfied the con...

The purpose of this paper is to present the applications of multidimensional fixed point theorems. For this, we provide two multidimensional fixed point theorems and then using these theorems, we prove the existence and uniqueness of solution of a nonlinear systems of matrix equations.

Complex vibration phenomena appear so frequently in many engineering and physical experiments, and they are well modeled using nonlinear differential equations. However, contrary to the linear models, nonlinear models are difficult to analyze analytically or numerically and particularly for long-time spans. In this paper, we propose a novel method...

in this paper, we develop and analyze the use of the Differential transformation method (DTM) to find the semi analytical solution for high order fuzzy initial value problems (FIVPs) involving ordinary differential equations. DTM allows for the solution of FIVPs to be calculated in the form of an infinite series by which the components will be simply c...

In this paper, we discuss the approximate solution of first order nonlinear fuzzy initial value problems (FIVP) by formulate and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM). OHAM allows for the solution of the fuzzy differential equation to be calculated in the form of an infinite series in which the components can be easily co...

The purpose of this paper is to study the Picard iterations of a Hermitian matrix operator. In [1], we proved the existence and uniqueness of attractive fixed point of an operator defined on Hermitian matrix space and satisfying a certain condition. In this paper we show that the n th Picard iterations of that Hermitian matrix operator converges to...

In this study, Homotopy Perturbation Method (HPM) is proposed, analyzed and developed to solve the fuzzy linear Cauchy reaction-diffusion equation with the fuzzy initial condition. HPM allows for the solution of the fuzzy linear Cauchy reaction-diffusion problem be calculated in the form of series function in which the ingredient can be easily dete...

In this paper, a new reliable algorithm called the multistage optimal homotopy asymptotic method (MOHAM) based on the standard optimal homotopy asymptotic method (OHAM) for solving secondorder nonlinear boundary value problems (BVPs) is presented. The new algorithm is a modification of the OHAM, in which it is based on partitioning the domain into...

In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of...

This paper discusses the use of biharmonic cubic Said-Ball surfaces in image enlargement area. Resizing an image through up sampling or down sampling is generally common for making smaller image fit a bigger screen in full screen mode or reducing a higher resolution image to a smaller resolution. However due to some limitation, this paper will focu...

In this paper, we develop and analyze the use of the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate analytical solution for partial differential equation involving fuzzy heat equation. OHAM allows the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be ea...

In this study, the Homotopy Perturbation Method (HPM) is modified and formulated to find the Semi analytical solution for an initial value problem involving the system of linear fuzzy differential equation. HPM allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easi...

The purpose of this paper is to present a numerical approach to solve fuzzy initial value problems (FIVPs) involving n-th order ordinary di�erential equations. The idea is based on the formulation of the six stages Runge-Kutta method of order �ve (RKM56) from crisp environment to fuzzy environment followed by the stability de�nitions and the conver...

In this paper, a new approximate analytical algorithm namely multistage optimal homotopy asymptotic method (MOHAM) is presented for the first time to obtain approximate analytical solutions for linear, nonlinear and system of initial value problems (IVPs). This algorithm depends on the standard optimal homotopy asymptotic method (OHAM), in which it...

In this work, the reliability allocation optimization problems in fuzzy environment have been developed and their result have also discussed. The numerical solutions of crisp reliability optimization problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method is de...

In this paper, the Adomian Decomposition Method (ADM) is employed to solve delay differential equations in the fuzzy case (FDDEs). The Adomian decomposition method can be used for solving nth order fuzzy delay differential equations directly without reduction to first order system. The illustration of capability of the method is implemented on seco...

In this paper a numerical method for solving Tow Point Fuzzy Boundary Value Problems '(TPFBVP) involving linear Emden Folwer equation is considered. The finite difference method (FDM) for solving TPFBVP is introduced and the proof of convergence of approximate solutions is brought in detail. Finally a numerical example is solved for illustrating th...

n this paper, we develop and analyze the use of the Homotopy Perturbation Method (HPM) to find the approximate analytical solution for an initial value problem involving the fuzzy parabolic equation. HPM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be eas...

In this paper, we develop and analyze the use of the Homotopy Perturbation Method (HPM) to find the approximate analytical solution for an initial value problem involving the fuzzy parabolic equation. HPM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be ea...

In this paper the optimal homotopy asymptotic method (OHAM) is employed to obtain approximate analytical solution of nth order linear fuzzy initial value problems (FIVPs). The convergence theorem of this method in fuzzy case is presented and proved. This method provides us with a convenient way to control the convergence of approximation series. Th...

In this work, the homotopy perturbation method is developed and formulated to find an approximate-analytical solution of fuzzy initial value problems involving a nonlinear first order ordinary differential equation. HPM allows for the solution of FIVPs to be calculated in the form of an infinite series in which the components can be easily computed...

In this paper we formulate a fifth order Runge-Kutta method for solution of fuzzy linear initial value problem involving ordinary differential equations with trapezoidal and triangular fuzzy numbers. We conduct an error analysis and perform numerical experiments. It is shown that method yielded very accurate results.

In this paper the Adomian Decomposition Method (ADM) is employed to solve nth order (n>2) non linear two point fuzzy boundary value problems (TPFBVP). The Adomian decomposition method can be used for solving nth order fuzzy differential equations directly without reduction to first order system. We illustrate the method in numerical experiment incl...

In this paper, we develop and analyze the use of the Variational Iteration Method (VIM) to find the semi- analytical solution for an initial value problem involving the fuzzy heat parabolic equation. VIM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be eas...

In this paper, we use the Variational Iteration Method (VIM) to find the approximate analytical solution for an initial value problem involving the fuzzy Duffing ordinary differential equation. VIM allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily computed....

In this paper, we use the Variational Iteration Method (VIM) to find the approximate analytical solution for an initial value problem involving the fuzzy Duffing ordinary differential equation. VIM allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily computed....

In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s...

In this paper, the Homotopy Analysis Method (HAM) is used to solve high order ( >=2 ) linear and non linear fuzzy initial value problems involving ordinary differential equations. This method allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily calculated. The...

In this work, the reliability optimization problem of the redundant system in fuzzy environment is developed and the results are discussed. The numerical solutions of crisp reliability optimization problems are compared and the fuzzy solution and its effectiveness are presented and discussed. The penalty function method has be developed and mixe...

In this work, the Homotopy Perturbation Method (HPM) is formulated to find a semi-analytical solution of the Fuzzy Initial Value Problem (FIVP) involving nonlinear second order Riccati equation. This method is based upon homotopy perturbation theory. This method allows for the solution of the differential equation to be calculated in the form of a...

In this paper the Optimal Homotopy Asymptotic Method (OHAM) is employed to solve n th order linear and non-linear two point fuzzy boundary value problems (TPFBVP) OHAM is different from other semi -analytical methods in that it gives extremely good results for even a large domain with minimal terms of the approximate series solution. Furthermo...

We employ the Adomian decomposition method to solve a high order linear fuzzy initial value problem involving ordinary differential equations. The Adomian decomposition method can be used for solving 4th order fuzzy differential equations directly without reduction to first order system. We illustrate the method in numerical experiment and compare...