Marwan Abukhaled

American University of Sharjah | AUS · Department of Mathematics and Statistics

Purpose: This study presents a novel application of the semianalytical residual power series method to investigate a one-dimensional fractional anisotropic curvature equation describing the human cornea, the outermost layer of the eye. The fractional boundary value problem, involving the fractional derivative of curvature, poses challenges that con...

The primary goal of this article is to present novel analytical solutions for the coupled nonlinear equation found in the mediated electron transfer process at polymer-modified conducting ultramicroelectrodes. Taylor’s series method is utilized to obtain approximate analytical solutions for the reaction-diffusion equations, allowing for the determi...

The impact of activation energy in chemical processes, heat radiations, and temperature gradients on non-Darcian steady MHD convective Casson nanofluid flows (NMHD-CCNF) over a radial elongated circular cylinder is investigated in this study. The network of partial differential equations (PDEs) for NMHD-CCNF is developed using the modified Buongior...

An electrochemical photobioreactor with a packed bed containing transparent gel granules and immobilized photosynthetic bacterial cells is shown with a one-dimensional two-phase flow and transport model. We consider the biological/chemical events in the electrochemical photobioreactor, the intrinsically connected two-phase flow and mass transport,...

In this paper, new types of M-fractional wave solutions of mathematical physics model named as truncated M-fractional (1+1)-dimensional non-linear simplified Modified Camassa-Holm model are achieved by applying the modified simplest equation (MSE), Sardar sub-equation and generalized Kudryashov techniques. The gained solutions containing dark, brig...

In this paper, Akbari-Ganji's and Taylor series methods are applied to find analytical solutions to nonlinear differential equations that arise in an immobilized-cell photobioreactor. Approximate analytical expressions for substrate and product concentrations and both liquid and gas phases for various parameter values are derived using both methods...

The primary goal of this article is to present novel analytical solutions for the coupled nonlinear equation found in polymer-modified conducting ultramicroelectrodes. Taylor's series method is utilized to obtain approximate analytical solutions for the reaction-diffusion equations, allowing for the determination of the substrate and mediator conce...

This article presents a theoretical analysis of homogeneous redox catalysis in electrochemical reactions. A nonlinear differential system is used as a model in which a nonlinear term is linked to homogeneous reactions. The concentration of the mediator and substrate at a planar electrode is computed using an analytical method under pure kinetic con...

Recently, conformable calculus has appeared in many abstract uses in mathematics and several practical applications in engineering and science. In addition, many methods and numerical algorithms have been adapted to it. In this paper, we will demonstrate, use, and construct the cubic B-spline algorithm to deal with conformable systems of differenti...

In this article, the analytical solutions of economically important model named as the Ivancevic option pricing model (IOPM) along new definition of derivative have been explored. For this purpose, exp a function, extended sinh-Gordon equation expansion (EShGEE) and extended G ′ / G -expansion methods have been utilized. The resulting solutions are...

The main purpose of this study was to produce abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation that represents unstable optical solitons that emerge from optical propagations through the use of birefringent fibers. These new types of soliton solutions have behaviors that are bright, dark, W-shaped, M-shaped, p...

This paper will introduce novel techniques for a fractional-order model of the human liver involving the Atangana–Baleanu, Atangana–Toufik, and the Fractal fractional method with the nonsingular kernel. These techniques give more accurate and appropriate results. Existence and uniqueness have been developed with the help of fixed-point theory resul...

This work aims to provide the numerical performances of the computer epidemic virus model with the time delay effects using the stochastic Levenberg-Marquardt backpropagation neural networks (LMBP-NNs). The computer epidemic virus model with the time delay effects is categorized into four dynamics, the uninfected S(x) computers, the latently infect...

A theoretical model of an amperometric biosensor with a modified electrode that inhibits the substance is addressed. The solution of a system of reaction-diffusion equations in a bounded region with a non-linear term similar to non-Michaelis- Menten kinetics of the enzymatic reaction is the basis for this model. The estimated analytical expression...

The Fitzhugh–Nagumo equation is an important non-linear reaction–diffusion equation used to model the transmission of nerve impulses. This equation is used in biology as population genetics; the Fitzhugh–Nagumo equation is also frequently used in circuit theory. In this study, we give solutions to the fractional Fitzhugh–Nagumo (FN) equation, the f...

The theoretical model for a packed porous catalytic particle of the slab, cylindrical, and spherical geometries shape in fixed-bed electrochemical reactors is discussed. These particles have internal mass concentration and temperature gradients in endothermic or exothermic reactions. The model is based on a nonlinear reaction–diffusion equation con...

Numerical treatment of the COVID-19 transposition and severity in Romania and Pakistan has been presented in this study, i.e., ANN-GA-SQP through artificial neural network genetic algorithms (ANN-GA) and sequential quadratic programming (SQP), a design of an integrated computational intelligent paradigm, COVID-19 is widely considered to be the grea...

The application of hybrid nanomaterials for the improvement of thermal efficiency of base fluid has increasingly gained attention during the past few decades. The basic purpose of this study is to investigate the flow characteristics along with heat transfer in an unsteady three-dimensional flow of hybrid nanofluid over a stretchable and rotatory s...

This article discusses a mathematical model of transport and reaction in multiscale porous biocatalytic electrodes using glucose oxidation catalyzed by glucose oxidase. The mathematical model, which is a system of two nonlinear differential equations, represents the diffusion and reaction within hydrogel film for the substrate and mediator assuming...

This paper discusses a complex nonlinear fractional model of enzyme inhibitor reaction where reaction memory is taken into account. Analytical expressions of the concentrations of enzyme, substrate, inhibitor, product, and other complex intermediate species are derived using Laplace decomposition and differential transformation methods. Since diffe...

Purpose The purpose of this study is to obtain an analytical solution for a nonlinear system of the COVID-19 model for susceptible, exposed, infected, isolated and recovered. Design/methodology/approach The Laplace decomposition method and the differential transformation method are used. Findings The obtained analytical results are useful on two...

In this contribution, a Langmuir–Hinshelwood–Hougen–Watson (LHHW) type kinetic model is discussed for simple one-dimensional geometry of porous catalysts such as a sphere, infinite cylinder, and flat pellets. The system is described in finite-range Fickian diffusion and nonlinear reaction kinetics to produce a nonlinear reaction–diffusion equation....

In this article, a mathematical model for a nonlinear roll motion of a ship is discussed and analytically solved. The model is a second-order nonlinear differential equation containing nonlinear terms of damping and restoring moments. Under normal or irregular waves, analytical expressions of roll angle, roll velocity, and moments of damping and re...

Background: Preventing substantial environmental hazards caused by noxious gases and solutes from sanitary landfills necessitates adequate regulations that require knowledge of the underlying mechanisms involved and the effect of various strategies. Mathematical models have been used to understand the development of landfill gas based on sequential...

A mathematical model of immobilized enzyme system in a porous planar, cylindrical, and spherical particle is discussed. The model is based on a nonlinear factor associated with reversible Michaelis–Menten kinetics of the enzyme process. The reliable semi-analytical is a special case of Akbari-Ganji method is used to solve the nonlinear reaction–dif...

Background A mathematical model for the combustion of ethanol and ethyl acetate mixtures using Mn 9 Cu 1 (mixture of manganese and copper with a weight ratio of 9:1) catalyst is discussed. The model’s kinetic mechanism is expressed in terms of nonlinear reaction-diffusion equations with common initial and boundary conditions in a finite planar, cyl...

A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji'...

A mathematical model of an amperometric biosensor response for uncompetitive inhibition detection is discussed. The model is based on a system of reaction–diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. Two highly accurate and easily accessible analytical methods are used to solve the...

A mathematical model of electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme is discussed. The model involves the coupled system of non-linear reaction–diffusion equations of substrate and hydrogen ion. The non-linear term in this model is related to the Michaelis–Menten reaction of the substrate and non...

A semi-analytical solution of the nonlinear boundary value problem that models the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit is presented. An integral operator expressed in terms of Green’s function is constructed then followed by an application of fixed point theory to generate a highly accu...

A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation. Analytical expressions for the roll angle, velocity, acceleration, and damping and restoring moments are derived using a modified approach of homotopy perturbation method (HPM). Also, the opera...

Mathematical models of ethanol fermentation in continuous conventional bioreactor (CCBR) and continuous membrane bioreactor (CMBR) are discussed theoretically. Each of these models is a system of nonlinear equations containing nonlinear terms related to Monod model for each retention time at non-steady condition. Analytical expressions of cell grow...

A convective-diffusion equation with semi-infinite boundary conditions for rotating disk electrodes under the hydrodynamic conditions is discussed and analytically solved for electrochemical catalytic reactions. The steady-state catalytic current of the rotating disk electrode is derived for various possible values of parameters by using a new appr...

In this paper, a mathematical model for the transmission dynamics of HIV/AIDS epidemic with emphasis on the role of female sex workers is considered. The model is a system of nine nonlinear differential equations that represent nine different groups of an HIV population. A modified approach of the homotopy perturbation method is used to derive an a...

A mathematical model of the magnetohydrodynamic free convective flow of a viscous incompressible fluid, which is based on a system of coupled steady-state nonlinear deferential equations, is discussed. A new approach of the homotopy perturbation method is employed to derive analytical expressions of the fluid velocity, fluid temperature, and specie...

In this article, the mathematical model presented by Barami and Ghafarinia (Sensors and Actuators B: Chemical 293 (2019) 31-40) for metal oxide grains is discussed. The nonlinear governing model, which is a Poisson-Boltzmann-type equation, is solved by a simple and efficient method. Analytical expressions for the electrical potential and oxygen ion...

A thorough study of the effects of ambient temperature and surface emissivity on the heat transfer of a conductive-radiative fin is presented in this article. A semi-analytical method based on Green’s function coupled with fixed point iterative schemes will be employed to solve a nonlinear energy equation that governs a straight rectangular fin. Th...

An efficient analytical method is applied to solve a system of convection-diffusion equations in the pseudo-first-order EC-catalytic mechanism at a rotating disk electrode. A simple closed form analytical expression for the concentration of oxidized and reduced catalyst species in the electrochemical reaction is obtained and analyzed for various va...

A mathematical model describing the reduction of Hydrogen peroxide (H2O2) to water in a metal dispersed conducting polymer film is discussed. The model is based on a system of reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. The approximate analytical expressions corresponding...

Analysis of the hysteresis of the enzyme-substrate due to enzyme flow calorimetry is presented based on the mathematical modeling of an immobilized enzyme using kinetic and diffusion parameters. The model is represented by ordinary differential equations containing a nonlinear term representing the substrate inhibition kinetics of the enzymatic rea...

A convective-diffusion equation with semi-infinite boundary conditions for rotating disk electrodes under the hydrodynamic conditions is discussed and analytically solved for electrochemical catalytic reactions. The steady-state catalytic current of the rotating disk electrode is derived for various possible values of parameters by using a new appr...

The mathematical model of Oldham1for rotating disc electrode in an unsupported system is discussed. This article presents a new analytical method for the calculation of concentration at a rotating disc electrode controlled by diffusion, convection and migration. This model contains a steady-state nonlinear differential equation in a three-ion syste...

We consider different distribution functions as possible fits for the light curves (time profiles) of Terrestrial Gamma-ray Flashes (TGFs): the piecewise Gaussian and the piecewise exponential, which correspond to the assumption of exponential growth and decay of the electrons that emit the radiation, and the inverse Gaussian and Ornstein-Uhlenbeck...

In this paper, a numerical approach is proposed to find a semi analytical solution for a prescribed anisotropic mean curvature equation modeling the human corneal shape. The method is based on an integral operator that is constructed in terms of Green’s function coupled with the implementation of Picard’s or Mann’s fixed point iteration schemes. Us...

In this paper, a Green’s function based iterative algorithm is proposed to solve strong nonlinear oscillators. The method’s essential part is based on finding an appropriate Green’s function that will be incorporated into a linear integral operator. An application of fixed point iteration schemes such as Picard’s or Mann’s will generate an iterativ...

In this paper, a constructed Green’s function coupled with a fixed point iteration scheme will be employed to solve nonlinear dynamical problems that arise in electroanalytical chemistry. More precisely, the method will be used to mathematically model and solve the kinetics of the ampermoetric enzyme. A main property that makes the proposed method...

In this study, a new algorithm based on Green's function fixed point iterations is developed and implemented to solve a class of nonlinear boundary value problems that arise in heat transfer. The method will be employed to determine the efficiency of convective straight fins with temperature dependent thermal conductivity. The main idea of this met...

The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supported plate will be minimized within a prescribed time duration using piezoelectric patches (voltages). The minimization...

The control of thermally induced vibrations of a rectangular plate is investigated. An optimization problem is formulated to determine the control voltage needed to perform vibration suppression with least control effort. By eigenfunction expansion, the optimal control problem will be converted from a distributed to a lumped parameter system. By ut...

The control of the uptake of growth factors in tissue engineering is mathematically modelled by a partial differential equation subject to boundary and initial conditions. The main objective is to regulate cellular processes for the growth or regeneration of a tissue within an assigned terminal time. The techniques of basis function expansion and d...

Maximum likelihood fits for the time profiles of 51 terrestrial gamma-ray flashes (from CGRO/BATSE and FGST/GBM) were calculated for five proposed probability densities. A lognormal distribution, which had been used by other researchers (e.g. [Briggs et al., 2010]), was compared with piecewise-Gaussian, piecewise-exponential, inverse-Gaussian, and...

The control of thermally induced vibrations of a rectangular plate is investigated. An optimization problem is formulated to determine the control voltage needed to perform vibration suppression with least control effort. By eigenfunction expansion, the optimal control problem will be converted from a distributed to a lumped parameter system. By ut...

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a single piezoelectric actuator. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combina...

The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral...

This paper presents the vibration control of a thermoelastic rectangular plate subjected to sudden heat inputs. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time with the least expenditure of control forces. The solution method is a combination of a modal expans...

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accura...

Under the infinite logarithmic matrix norm, a criterion for mean square stability of second-order weak numerical methods for multi-dimensional stochastic differential systems is established. Numerical examples are demonstrated to support the theoretical results.

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a single piezoelectric actuator. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combina...

Two numerical schemes for finding approximate solutions of singular two-point boundary value problems arising in physiology are presented. While the main ingredient of both approaches is the employment of cubic B-splines, the obstacle of singularity has to be removed first. In the first approach, L’Hopital’s rule is used to remove the singularity d...

Galerkin and wavelet methods for optimal boundary control of a couple of discretely connected parallel beams are proposed. First, the problem with boundary controls is converted into a problem with distributed controls. The problem is, then, reduced by a Galerkin-based approach into determining the optimal control of a linear time-invariant lumped...

The control of the uptake of growth factors in tissue engineering is mathematically modeled via a partial differential equation subject to boundary and initial conditions. The main objective is to regulate cellular processes for the growth or regineration of a tissue within an assigned terminal time. CAS wavelets approach is proposed to solve the o...

A numerical approach based on cubic spline collocation is presented to obtain an approximate solution for a class of boundary value problems. Under quite general restrictions, the method is shown to be of second-order accuracy. Numerical examples are given to demonstrate the utility and efficiency of the proposed method and to confirm the second-or...

This paper considers the problem of controlling the solution of an initial boundary-value problem for a wave equation with time-dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performan...

A proposed computational method is applied to damp out the excess vibrations in smart microbeams, where the control action is implemented using piezoceramic actuators. From a mathematical point of view, we wish to determine the optimal boundary actuators that minimize a given energy-based performance measure. The minimization of the performance mea...

The optimal control of transverse vibration of two Euler–Bernoulli beams coupled in parallel by discrete springs is considered. An index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces. The minimization of the performan...

In recent years, many numerical methods for solving stochastic differential equations have been developed. Some of these methods converge in the weak sense and some others converge in the mean square sense. One of the important features of numerical methods is their stability behavior. In this paper, we focus our attention on stability in expectati...

The optimal control of a distributed system consisting of two Euler-Bernoulli beams coupled in parallel with pointwise controllers is considered. The optimal control problem is to minimize a given performance index over these forces and subject to the equation of motion governing the structural vibrations, the imposed initial condition as well as t...

We study (linear) negacyclic codes, i.e., ideals in the ring D 4 =Z 4 [x]/〈x n +1〉, of even length n. We find the set of generators for this type of code. It is shown that any negacyclic code has the form 〈α(x+1) m 〉, where α=1 or 2, and m∈{0,1,⋯,n-1}. It is also shown that the element 2 is in every nonzero code of the form 〈(x+1) m 〉. As such, we...

The optimal control of a distributed host structure consisting of two Euler-Bernoulli beams coupled in parallel with boundary controllers is considered. An index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving boundary control forces. The minim...

The logarithmic matrix norm with respect to l2 matrix norm will be used to investigate mean square stability for a class of second-order weak schemes when applied to 2-dimensional linear stochastic differential systems with one multiplicative noise. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Despite the intensive work done on developing numerical schemes for stochastic differential equations, stability analysis of these schemes when applied to stochastic differential systems is still under premature stage. Motivated by the work of Saito and Mitsui in [11], we investigate mean square stability for a class of weak second order Runge-Kutt...

Recent years have marked many significant advances in numerical treatments for stochastic differential equations. Emphasis was not only on the nature and order of convergence of numerical schemes, but also on their stability features [J. Comput. Appl. Math. 125 (2000) 171; BIT 33 (1993) 654; Comput. Math. Appl. 28 (1994) 45; SIAM J. Appl. Anal. 51...

The optimal control of a distributed system consisting of two Euler–Bernoulli beams coupled in parallel with pointwise controllers is considered. An index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces. The minimizatio...

A deterministic approach for solving stochastic differential equations is described and numerically tested. In this approach, probability distributions of the sample paths at successive time steps in a numerical procedure are shown to satisfy a recursive integral equation. These probability distributions are approximated by solving the integral equ...

A class of explicit Runge-Kutta methods for numerical solution of stochastic differential equations is described, analyzed, and numerically tested. It is shown that this class is of second-order accuracy in the weak sense. Also, a varaince reduction technique is presented that reduces the stochastic error involved when computing expectations. Numer...