Sunil Dutt Purohit

Rajasthan Technical University · Department of HEAS (Mathematics)

This book focuses on the fundamental processes involved in calcium signaling through fractional mathematical modeling. The intended reader of the book is mathematically proficient students of cell biology, applied mathematics and mathematical biology who are interested in learning about modeling in cell biology. The book inspires the graduate stude...

In this study, we investigate novel fractional tuberculosis model with Caputo fractional derivative. The computational solution of the fractional tuberculosis disease is obtained with the help of the generalized Euler's method (GEM). This article considers two treatment strategies: protective treatment for latent populations and main treatment for...

The majorization property plays a significant role in understanding the behavior of certain classes of analytic functions and their mappings. In this research, we introduce two novel classes of analytic functions, denoted as Sζ[E, F; μ; γ] and Tζ(θ, μ, γ) using the usual operator Hs. Our primary focus is to investigate the majorization properties o...

In this study, we examine some expansion computations of the fractional calculus with the incomplete \(\aleph \)-function via the Leibniz rule. The \(\aleph \)-function, incomplete I-function, and incomplete H-function expansion calculations are also identified as exceptional examples of our main findings.

The Navier–Stokes equation is a key governing equation for the motion of viscous fluid flow. The main target of our work is to obtain the solution to multi-dimensional Navier–Stokes equations in the Yang–Abdel–Cattani fractional sense. The results of the model are in terms of the three-parameter Prabhakar function. Three examples are discussed that...

This study focuses on improving the accuracy of assessing liver damage and early detection for improved treatment strategies. In this study, we examine the human liver using a modified Atangana-Baleanu fractional derivative based on the mathematical model to understand and predict the behavior of the human liver. The iteration method and fixed-poin...

In this paper, q-analogues of the Sumudu transform, along with an inversion formula and some explicit computations, are presented. This work essentially focuses on q-analogues of the inverse Sumudu transform and the construction method of the inversion formula via a path integral along a Bromwich contour. It is also shown how the complex inversion...

Since, receptor plays significant role in calcium signalling and to understand the mechanism of signalling in detail; an essential component is the mechanism of receptor activation. The mobilization of intracellular calcium from intracellular stores depends upon binding of the agonist to the cell surface receptor. In this chapter to understand thro...

In this chapter, we study the change in cellular calcium with different buffers. The study is carried over the advection–diffusion equation framed for the cellular calcium with inclusion of buffers. The level of cellular calcium gets lowered down in the presence of buffers. Buffers bind to the free calcium ions and play a vital role in lowering the...

In this chapter, we investigate calcium signaling in cardiac myocytes. Calcium is a critical regulator of cardiac myocyte functions. Here, we develop a mathematical model to describe the calcium transients in cardiac myocytes. Since diffusion is a basic transport process involved in the evolution of many non-equilibrium systems toward equilibrium,...

This chapter aims to familiarize the reader with the new field of mathematics known as ‘fractional calculus’, as well as the operators, techniques, and additional mathematical definitions that will be useful in the work that will be covered in subsequent chapters. A significant component of contemporary biological research is its dependence on comp...

The Bernoulli equation is useful to assess the motility and recovery rate with respect to time in order to measure the COVID-19 outbreak. The homotopy perturbation method was applied in the current article to compute the Bernoulli equation. For the existence and uniqueness of solutions, we also used the Caputo–Fabrizio Integral and differential ope...

Due to the high importance of the convection-diffusion equation, we aim to develop a quadratic upwind differencing scheme in the finite volume approach for solving this equation. Our newly developed numerical approach is conditionally stable. The strategy employs a quadratic upwind differencing scheme in the finite volume technique for spatial ap...

The generalized fractional calculus operators introduced by Saigo and Maeda in 1996 will be examined and further explored in this paper. By combining an incomplete ℵ-function with a broad category of polynomials, we create generalized fractional calculus formulations. The findings are presented in a concise manner that are helpful in creating certa...

The parallel and distributed processing are becoming de facto industry standard, and a large part of the current research is targeted on how to make computing scalable and distributed, dynamically, without allocating the resources on permanent basis. The present article focuses on the study and performance of distributed and parallel algorithms the...

Mathematical models have been employed to investigate the factors that govern the progression of infectious diseases in viral infections. This article investigates a fractionalised model for hepatitis B virus infection, curing infected cells. We analysed the fractional hepatitis B virus infection model using the homotopy decomposition method (HDM)....

The study discussed in this article is driven by the realization that many physical processes may be understood by using applications of fractional operators and special functions. In this study, we present and examine a fractional integral operator with an I-function in its kernel. This operator is used to solve several fractional differential equ...

The log-based analysis and trouble-shooting has remained prevalent and commonly used approach for centralized and time-haring systems. However, for parallel and distributed systems where happen-before relations are not directly available between the events, it become a challenge to fully depend on log-based analysis in such instances. This article...

Calcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fraction...

In this study, we present and examine a fractional integral operator with an I$$ I $$‐function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has a set of particular cases whose solutions represent different physical phenomena. Much mathematical physics, biology, engineering, and chemistry proble...

In the present work, we investigate five new generalised integral formulae by involving the extension form of the Hurwitz-Lerch zeta function and obtain the results in the form of a hypergeometric function in product form by using the properties of the Hadamard product , from which two power series emerge. Furthermore, we also address their special...

Novel corona disease is spreading all over the world. The cases of the corona virus are increasing drastically day by day. Therefore, it is necessary to predict the cases in advance to handle the condition. Recently, machine learning comes into the picture of researchers to solve the problem in engineering. The present study is focused to the appli...

The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete $ \bar {I} $ I¯-function (I $ \bar {I} $ I¯F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fracti...

Elzaki decomposition method (EDM) is adopted to deal with the fractional-order relaxation and damped oscillation equation along with time-fractional spatial diffusion biological population model in different suitable habitat situations. In accordance with the graphs for the solutions obtained, the fractional relaxation exhibits super-slow phenomeno...

In this paper, we determine certain coefficient inequalities for the classes of q-starlike and q-convex function and find the sufficient conditions for normalized basic hypergeometric function to belonging in these classes. The technique developed in this present investigations can be used with other functions.KeywordsDifferential subordinationUniv...

The aim of this paper is to present two composition formulae of pathway fractional integral (PFI) operators connected with altered extensions of the Bessel-Maitland function. We point out pertinent connections of certain particular cases of our main results with known results.

The goal of this paper is to develop some differential equation formulas for the extended generalized Mittag-Leffler function (EGMLF) using Caputo type Marichev-Saigo-Maeda (MSM) fractional derivative operators involving the third Appell function as kernel, with the results viewed in the context of extended Wright hypergeometric type function. Furt...

Objective of the present investigation is intended to study the MHD Casson fluids flow through an exponentially stretching surface. This free convective flow is in­vestigated in thermally stratified porous medium. Also viscosity along with thermal conductivity is varying with temperature. With the exponential decay for the inter­nal heat generation...

Multi-core design intends to serve a large market with user-oriented and highproductivity management as opposed to any other parallel system. Small numbers of processors, a frequent feature of current multi-core systems, are ideal for future generation of CPUs, where automated parallelization succeeds on shared space architectures. The multi-core c...

In the present work, a novel and even more generalized fractional kinetic equation has been formulated in terms of polynomial weighted incomplete H-function, incomplete Fox-Wright function and incomplete generalized hypergeometric function, considering the importance of the fractional kinetic equations arising in the various science and engineering...

In this paper we determine certain coefficient inequalities for the classes of q-starlike and q-convex function and find the sufficient conditions for generalized Bessel function to belonging in these classes.

In this study, an effort is made to develop mathematical models that may be used to explain the distribution of drug administration in the human body after oral and intravenous administration of the drug. The diffusion process was utilized to create three models, applying Fick’s principle and the law of mass action. The Sumudu transform algorithm a...

This study proposes a new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks by categorizing infected people into non-vaccinated, first dose-vaccinated, and second dose-vaccinated groups and exploring the transmission dynamics of the disease outbreaks. We present a non-linear integer order mathematical model of C...

Mathematical models have been used to understand the factors that control infectious disease progression in viral infections. This work considers a fractionalized model for HBV infection treating infected cells. Initially, the Hilfer fractional model has been developed for the epidemic problem. In this article analyzed the fractional form of the mo...

Gasper followed the fractional calculus proof of an Erdélyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulation-based proof of the Erdélyi integral, due to “Joshi and Vyas”. Motivated from this alternative wa...

Ethiopia is one of the countries highly affected by the COVID-19 pandemic in Africa. A new study has looked at the transmission dynamics of the outbreak in Ethiopia based on the age categories of the infected individuals. Infected individuals are divided into three age categories (less than 14 years (I $ _{1} $ 1), 15–54 years (I $ _{2} $ 2), and a...

In this paper, we determine the radius of λ-uniform convexity, λ-starlikeness, and α-convexity of order δ for the Weierstrass canonical product of an entire function as a root having smallest modulus and argument ϕ of a functional equation. As special cases, we also determine the radius of λ-uniform convexity, λ-starlikeness, and α-convexity of ord...

The paper's main aim is to investigate the 2019 coronavirus disease in Ethiopia using a fractional-order mathematical model. It would also focus on the importance of fractional-order derivatives that may help us in modelling the system and understanding the effect of model parameters and fractional derivative orders on the approximate solutions of...

Karst aquifers have a very complex flow system because of their high spatial heterogeneity of void distribution. In this manuscript, flow simulation has been used to investigate the flow mechanism in a fissured karst aquifer with double porosity, revealing how to connect exchange and storage coefficients to the volumetric density of the highly perm...

The goal of this article is to figure out the electric circuit responses under an impressed voltage E0 f(w) associated with incomplete I-functions and incomplete Ī-functions. The analytical solutions for the RLC, RC and RL circuit are derived using the Laplace transform approach. (2010) Mathematics Subject Classifications: 33B20; 33E20; 26A33.

The goal of this article is to figure out the electric circuit responses under an impressed voltage E0 f(w) associated with incomplete I-functions and incomplete ī-functions. The analytical solutions for the RLC, RC and RL circuit are derived using the Laplace transform approach. (2010) Mathematics Subject Classifications: 33B20; 33E20; 26A33.

The purpose of this research is to investigate the result of Katugampola kinetic fractional equations containing the first kind of generalized Bessel's function. This paper considers the manifold generality of the first kind generalized Bessel's function in form of the solution of Katugampola kinetic fractional equations. The $\tau$ Laplace transfo...

The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control . The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population i...

In the present paper, we derive two theorems involving fractional q-integral operators of Erdelyi-Kober type involving the basic analogue of the I-function of two variables. Corresponding assertions for the Riemann-Liouville and Weyl fractional q-integral transforms are also presented. Several special cases of the main results have also been illust...

We use the q-homotopy analysis Shehu transform method in this article to obtain analytical and numerical solutions to time fractional partial differential equations. We also give analytical solutions to two problems, as well as a comparison study in terms of absolute error with homotopy perturbation transform method, homotopy analysis transform met...

In this article, we find the numerical solution of unsteady state fractional order advection-dispersion equation. For an approximate solution of the proposed problem, we apply Laguerre spectral collocation method and the idea of finite difference method. The proposed method assisted us in reducing the fractional order unsteady state advection-dispe...

Many researchers are interested in Lambert's law because of its relevance in light attenuation owing to the characteristics of a material through which the light passes. In this paper, we developed the Lambert’s law that involves incomplete I-functions. Next, while taking a course in the constraints of incomplete I-functions, we give a few special...

The aim of this paper is to generalize the Landau-type Tauberian theorem for the bicomplex variables. Our findings extend and improve on previous versions of the Ikehara theorem. Also boundedness result for the bicomplex version of Ikehara–Korevaar theorem is derived. The purpose of this article is to substantially extend the various complex Tauber...

The present study examines the impacts of chemical reactions over an exponentially expanding sheet of viscous incompressible fluid flow in a porous medium with the imposed magnetic field. Here reaction rate and wall concentration are exponential variables. The basic equations of the governing flow are transformed into ordinary differential equation...

The aim of this study is to investigate the flow of two distinct nanofluids over a stretching surface in a porous medium with Marangoni convection. This investigation is studied under the effect of thermal radiation. Here, we have considered Fe3O4 and ZrO2 nanosized particles suspended in engine oil (EO) base fluid. For the numerical simulation of...

Special functions and fractional calculus are significant in the study of differential equations and their solutions, and then as a result, they are linked to a broad variety of issues in science and engineering. The Marichev-Saigo-Maeda (MSM) fractional order differential and integral formulae for the combination of generalised Srivastava polynomi...

Several techniques, including mathematical models, have been explored since the onset of COVID-19 transmission to evaluate the end outcome and implement drastic measures for this illness. Using the currently infected, noninfected, exposed, susceptible, and recovered cases in the Indian community, we created a mathematical model to describe the tran...

The aim of this investigation is to study hybrid nanofluid flow past a permeable stretching sheet in is presented. With heat source/sink and uniform magnetic field the flow is investigated in porous medium. A suspension of Copper Oxide-Silver nanoparticles in an ethanol glycol based fluid with Marangoni convection is considered. The mathematical mo...

The present paper deals with four new generalized integral formulae involving product of Srivastava's polynomials and generalized multiindex Bessel function and are represented in terms of the Fox-Wright function. Various particular cases and consequences of our main results involving the Hermite polynomials are also pointed out.

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature...

The impact of heat and mass transfer were analyzed in the present investigation by considering the peristaltic transport of a Jeffery fluid with nanoparticles in a uniform tube. Lubrication theory hypotheses have been considered and expressions have been defined for axial velocity, pressure drop, frictional force, heat and mass transfer effects. Th...

The main purpose of this paper is to introduce general families of the extended Mathieu‐type power series and present a number of potentially useful integral representations of several general families of the extended Mathieu‐type power series in a unified manner. Relationships of the extended Mathieu‐type functional power series with the generaliz...

In this paper, we have studied a unified multi-index Mittag–Leffler function of several variables. An integral operator involving this Mittag–Leffler function is defined, and then, certain properties of the operator are established. The fractional differential equations involving the multi-index Mittag–Leffler function of several variables are also...

The aim of this paper is to study the calcium profile governed by the advection diffusion equation. The mathematical and computational modeling has provided insights to understand the calcium signalling which depends upon cytosolic calcium concentration. Here the model includes the important physiological parameters like diffusion coefficient, flow...

The motive of the current investigation is to present a comparative study of entropy generation on Newtonian and Non-Newtonian fluids. Heat transfer of the slip flow over a melting expending surface, is investigated with an imposed heat source and non-uniform radiation. Uniform inclined magnetic field is also applied and medium is considered porous...

In this paper, we have determined some integral formulae of incomplete I-functions involving the exponential function, the Legendre polynomials and generalized Laguerre polynomials.

Through applying the Kober fractional q-calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q-integral operator in the open disk. The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded addressed immediate...

In this article, for the incomplete H -functions, we obtain a set of new generating functions. The bilateral along with linear generating relations are derived for the incomplete H -functions. Many of the generating functions readily accessible in the literature are often deemed as implementations of the main findings. All the derived findings are...

The aim of this study is to investigate the heat transfer effect of γ–Al2O3 nanofluid flow with Marangoni convection over a porous stretching surface. Here, the aligned magnetic field is also considered. Ethylene glycol ( C 2 H 6 O 2 ) and water ( H 2 O ) are taken as base fluids. Thermal radiation is incorporated nonlinearly for the temperature fi...

In this study, we familiarise a novel class of Janowski-type star-like functions of complex order with regard to (j, k)-symmetric points based on quantum calculus by subordinating with pedal-shaped regions. We found integral representation theorem and conditions for starlikeness. Furthermore, with regard to (j, k)-symmetric points, we successfully...

Many textile industries produce waste water containing direct dyes, which often causes serious environmental problems. It has revealed from several studies that the absorption process in dye degradation follows a unique fractional property. As a result, the focus of this research is on fractional mathematical modeling of color textile effluents deg...

Our aim is to study and investigate the family of $(p, q)$ ( p , q ) -extended ( incomplete and complete ) elliptic-type integrals for which the usual properties and representations of various known results of the ( classical ) elliptic integrals are extended in a simple manner. This family of elliptic-type integrals involves a number of special ca...

The present analysis explores an analytical treatment for the computation of Poiseuille flow of a micropolar fluid in a channel placed in between two horizontal parallel plates. Both the plates are placed at constant wall temperatures. Therefore, the flow region is portioned into two different zones named zone I and zone II. Eringen’s micropolar fl...

Purpose The purpose of this paper is to study the comparative analysis between three hybrid nanofluids flow past a permeable stretching surface in a porous medium with thermal radiation. Uniform magnetic field is applied together with heat source and sink. Three set of different hybrid nanofluids with water as a base fluid having suspension of Copp...

An investigation is carried out on the analysis of entropy on the flow of non‐Newtonian fluid, in particular, micropolar fluid past an inclined channel. To enhance the fluid properties, velocity and thermal slip conditions are taken into consideration. At the outset, the novelty of the present investigation lies on the analysis of entropy generatio...

In this paper, we determine some expansion formulae of the incomplete I-functions in affiliation with the Leibniz rule for the Riemann-Liouville type derivatives. Further, expansion formulae of the incomplete $\overline{I}$-function, incomplete $\overline{H}$-function, and incomplete H-function are conferred as extraordinary instances of our primar...

The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type...

Through applying the Kober fractional -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a -differintegral operator in the open disk . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed...

Textile dyes are untreated discharge into the environment which results in a significant increase in water pollution levels worldwide. Due to the continuous addition of toxic organic dyes, a necessary strategic model is required for the complete degradation of dyes in textile effluent. This paper considers the possibility of biological synthesis of...

In this article, we introduce and investigate a new class of Bazilevič functions with respect to k-symmetric points defined by using fractional q-calculus operators that are analytic in the open unit disk D. Several interesting subordination problems are also derived for the functions belonging to this new class.

The paper examined the analysis of the effects on environmental pollution and the occurrence of biological populations by presenting a mathematical model for an incomplete I-function. The findings presented in this article are characteristic of physical sciences, and in a number of cases indicate interest in related parameter conditions.

The aim of the present investigation is to establish the composition formulas for the pathway fractional integral operator connected with Hurwitz-Lerch zeta function and extended Wright-Bessel function. Some interesting special cases have also been discussed.

Women’s security is still a big issue in our society. Women in the rural Rajasthan are very hard working; they spend their day in farms and also manage household stuff. To provide safety to the woman, an ornament worn by them could be modified with the design named ‘Borla’ suggested here. This ornament is having an e-wearable security system so tha...

In this article, we have studied solutions of a generalised multiorder fractional partial differential equations involving the Caputo time‐fractional derivative and the Riemann–Liouville space fractional derivatives using Laplace–Fourier transform technique. Proposed generalised multiorder fractional partial differential equation is reducible to Sc...

The object of this paper is to derive the expansion formulae for incomplete H-function and incomplete H-function. Further, their special cases are also point out in terms of different type of special functions (Meijer's (Γ) G-function, incomplete Fox-Wright pΨ (Γ) q-function and incomplete hyper-geometric function) which are general in nature and v...

Applying the concept of fractional q-calculus, we introduce the subclass T S m q (δ, λ, α, β) of β-uniformly starlike and β-uniformly convex functions involving a linear multiplier fractional q-differintegral operator. A characterization of those functions belonging to the newly-introduced subclass T S m q (·) is provided. Results on growth and dis...

In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace transform, Whittaker transform, K-transform and Fourier transforms. Also found the applications of the problem on fractional kinetic equation pertaining to the generalized...

This book gathers selected papers presented at 3rd International Conference on Communication and Computational Technologies (ICCCT 2021), jointly organized in virtual format by Rajasthan Institute of Engineering and Technology, Jaipur and Rajasthan Technical University Kota in association with Soft Computing Research Society, during 27–28 February...

In this paper, we investigate the fractional derivatives and expansion formulae of incomplete H and H-functions for one variable. Further, we also obtain results for repeated fractional order derivatives and some special cases are also discussed. Various other analogues results are also established. The results obtained here are very much helpful f...

The study of calcium dynamics is an important aspect as it regulates various processes viz metabolism, secretion etc. and also play the key role of second messenger. In the present work our main focus is over the variation of the cellular calcium with the various buffers after solving the advection-diffusion equation for the cellular calcium with i...

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In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral ope...