# Hossein JafariUniversity of Mazandaran University of South Africa

Hossein Jafari

Professor

## About

355

Publications

115,278

Reads

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10,800

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Introduction

Additional affiliations

December 2006 - December 2010

June 2003 - December 2006

Education

June 2003 - December 2006

September 1998 - January 2001

September 1994 - June 1998

## Publications

Publications (355)

In this paper, we obtain the exact solutions of Lienard equation using (G'/G)-expansion method. The solutions obtained here are expressed in hyperbolic functions. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in obta...

In this paper, the simplest equation method has been used for finding the exact solutions of three nonlinear evolution equations, namely the Vakhnenko–Parkes equation, the generalized regularized long wave equation and the symmetric regularized long wave equation. All three of these equations arise in fluids science, so finding their exact solution...

The equations of magnetohydrostatic equilibria for plasma in a gravitational field are investigated analytically. An investigation of a family of isothermal magneto static atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. The distributed current in the model J is directed al...

This study introduces a family of root-solvers for systems of nonlinear equations, leveraging the Daftardar-Gejji and Jafari Decomposition Technique coupled with the midpoint quadrature rule. Despite the existing application of these root solvers to single-variable equations, their extension to systems of nonlinear equations marks a pioneering adva...

The time fractional Black-Scholes equation (TFBSE) is designed to evaluate price fluctuations within a correlated fractal transmission system. This model prices American or European put and call options on non-dividend-paying stocks. Reliable and efficient numerical techniques are essential for solving fractional differential models due to the glob...

In this paper, approximate solutions for stochastic Fitzhugh–Nagumo partial differential equations are obtained using two‐dimensional shifted Legendre polynomial (2DSLP) approximation. The problem's suitability and solvability are confirmed. The convergence analysis for the proposed methodology and the error analysis in the L2$$ {L}^2 $$ norm are c...

The present study aims to introduce a numerical approach based on the hybrid of block-pulse functions (BPFs), Bernoulli polynomials (BPs), and hypergeometric function for analyzing a class of fractional variational problems (FVPs). The FVPs are made by the Caputo derivative sense. To analyze this problem, first, we create an approximate for the Rie...

In this paper, we use the local fractional variational iteration transform method LFVITM to solve a class of linear and nonlinear partial differential equations (PDEs), as well as a system of PDEs which are involving local fractional differential operators (LFDOs). The technique combines the variational iteration transform approach and the Yang–Lap...

In this paper, the Local Fractional Laplace Decomposition Method (LFLDM) is used for solving a type of Two-Dimensional Fractional Diffusion Equation (TDFDE). In this method, first we apply the Laplace transform and its inverse to the main equation, and then the Adomian decomposition is used to obtain approximate/analytical solution. The accuracy an...

Multi-term time fractional equations are designed to give a more accurate and flexible mathematical model for explaining the behavior of physical systems with complex dynamics over time. This model is a generalization of the classical Convection-Diffusion equations (CDEs) which time terms is considered by Caputo's time derivative sense for (0 < ≤ 1...

This paper proposes a method for solving fractional partial difference equations using discrete Sumudu transformation. Some properties of discrete Sumudu transformation were used. The applications of the test examples for the initial value problems of fractional partial difference equations were tested using two methods: the successive approximatio...

In this paper, we study the two-parameter spectral element method based on weighted shifted orthogonal polynomials for solving singularly perturbed diffusion equation on an interval [0, 1] which are modeled with singular parameters. We continue our study to estimate the lower bound of the weighted orthogonal polynomial coefficient and the upper bou...

Recently, modeling problems in various field of sciences and engineering with the help of fractional calculus has been welcomed by researchers. One of these interesting models is a brain tumor model. In this framework, a two dimensional expansion of the diffusion equation and glioma growth is considered. The analytical solution of this model is not...

In this article, we used some methods to solve Riemann-type fractional difference equations. Firstly, we use a method that is a composite method based on the successive approximation method with the Sumudu transform. Secondly, we use a method that is a composite method that consists of the homotopic perturbation method with the Sumudu transform. It...

In this paper, Darbo’s fixed point theorem is generalized and it is applied to find the existence of solution of a fractional integral equation involving an operator with iterative relations in a Banach space. Moreover, an example is provided to illustrate the results.

The main idea in this research is introducing another approximate method to calculate solutions of the fractional Torsion equation, which is one of the applied equations in civil engineering. Since the fractional order is closed to an integer, we convert the fractional Torsion equation to a perturbed ordinary differential equation involving a small...

The study of nonlinear oscillators is an important topic in the development of the theory of dynamical systems. In this research, a nonlinear fractional model is introduced, which is called the fractional Van der Pol model. This modified model is derived using the Caputo–Fabrizio operator. Achieving the solution of this model is not easy. Therefore...

This research paper investigates the SIZR model for Zombie infection outbreaks with a time-dependent infection rate. The proposed model is extended to the fractional order using different fractional derivative operators. The solution of the proposed model by numerical schemes, is briefed. Graphical representations provide us with a better understan...

In this paper, we introduce the notion of weak Wardowski contractive multivalued mappings and investigate the solvability of generalized '-Caputo snap boundary fractional differential inclusions. Our results utilize some existing results regarding snap boundary fractional differential inclusions. An example is given to illustrate the applicability...

In this paper, we develop a numerical method by using operational matrices based on Hosoya polynomials of simple paths to find the approximate solution of diffusion equations of fractional order with respect to time. This method is applied to certain diffusion equations like time fractional advection-diffusion equations and time fractional Kolmogor...

It is possible to obtain insight into recovery, the rate of moralities, and the spread of diseases, as well as transmission by mathematical modeling. This chapter discusses a dynamic system for the estimation of COVID-19 spread profile, with regard to factors such as social distancing and vaccination. An extended SEIR model is constructed, and its...

In this study, we propose an approximate solution based on two‐dimensional shifted Legendre polynomials to solve nonlinear stochastic partial differential equations with variable coefficients. For this purpose, we have considered a Fisher‐Kolmogorov‐Petrovsky‐Piskunov (Fisher–KPP) equation with space uniform white noise for the same. New stochastic...

An efficient high-order computational procedure is going to be created in this paper to determine the solution to the mobile–immobile advection–dispersion model (MIAD) of temporal fractional order [Formula: see text], which can be employed to model the solute forwarding in watershed catchments and floods. To do it, the temporal-first derivative of...

In the fuzzy calculus, the study of fuzzy differential equations (FDEs) created a proper setting to model real problems which contain vagueness or uncertainties factors. In this paper, we consider a class fuzzy differential equations (FFDEs) with non-integer or variable order (VO). The variable order derivative is defined in the Atangana–Baleanu–Ca...

In this paper, two algebraic methods are applied for solving a class of conformable fractional partial differential equations (FPDEs). We use these methods for the time-fractional Radhakrishnan–Kundu–Lakshmanan equation. With these methods, further solutions can be obtained compared with other approaches and techniques. The exact particular solutio...

In this paper, we study time-fractional diffusion equations such as the time-fractional Kolmogorov equations (TF–KEs) and the time-fractional advection–diffusion equations (TF–ADEs) in the Caputo sense. Here, we have developed the operational matrices (OMs) using the Hosoya polynomial (HP) as basis function for OMs to obtain solution of the TF–KEs...

This paper deals with a class of fractional variational problems involving Atangana–Baleanu (AB) derivative. The problem under consideration is a graceful combination of AB derivative with indefinite integral. A proposed numerical technique based on the shifted Vieta–Lucas polynomials is utilized for obtaining the solutions to the given problem. Ou...

In this study, we apply the fractional Laplace variational iteration method (FLVIM), a computer methodology for exploring fractional Navier–Stokes equation solutions. In light of the theory of fixed points and Banach spaces, this paper also explores the uniqueness and convergence of the solution of general fractional differential equations obtained...

In this article, we extended operational matrices using orthonormal Boubaker
polynomials of Riemann-Liouville fractional integration and Caputo
derivative to find numerical solution of multi-term fractional-order
differential equations (FDE). The proposed method is utilized to convert FDE
into a system of algebraic equations. The convergence of the...

In this work, an efficient variable order Bernstein collocation technique,
which is based on Bernstein polynomials, is applied to a non-linear coupled
system of variable order reaction-diffusion equations with given initial
and boundary conditions. The operational matrix of Bernstein polynomials is
derived for variable order derivatives w.r.t. time...

In this article, we propose a new technique based on 2-D shifted Legendre
polynomials through the operational matrix integration method to find the
numerical solution of the stochastic heat equation with Neumann boundary
conditions. For the proposed technique, the convergence criteria and the
error estimation are also discussed in detail. This n...

In this article, we obtain numerical solutions of Bagely-Torvik and a class of fractional oscillation
equations by using a numerical method based on Hosoya and Clique polynomials. The fractional derivative is in
the Coputo sense. In this method, first we convert the given fractional order differential equations to corresponding
fractional integral...

The deflection of Euler–Bernoulli beams under stochastic dynamic loading, exhibiting purely viscous behavior, is characterized by partial differential equations of the fourth order. This paper proposes a computational method to determine the approximate solution to such equations. The functions are approximated using two‐dimensional shifted Legendr...

This article presents an idea of a new approach for the solitary wave solution of the modified Degasperis–Procesi (mDP) and modified Camassa–Holm (mCH) models with a time-fractional derivative. We combine Laplace transform (LT) and homotopy perturbation method (HPM) to formulate the idea of the Laplace transform homotopy perturbation method (LHPTM)...

This paper deals with the study of a class of stochastic heat equation using the operational matrix of integration and stochastic integration based on two-dimensional shifted Legendre polynomials. The characteristics of these operational matrices together with the properties of shifted Legendre polynomials convert the stochastic heat equation into...

This paper proposes an approximate solution based on two-dimensional shifted Legendre polynomials, together with its operational matrices of integration and stochastic integration for solving stochastic Burgers’ equations with a space-uniform white noise and with variable coefficients. The aforementioned operational matrices transform the problem u...

In the context of decision support systems, bi-capacities were introduced as an extension of classical capacities. Many bipolar fuzzy integrals related to the bi-capacities have been presented in recent years. One of these integrals is the Sugeno integral concerning aggregation on bipolar scales. The paper aims to build an equivalent representation...

We apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the boundary and initial conditions. The ultimate goal of the algorithm is to set up a system of equations whose number matches the...

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The approximate solution takes the form of a product consisting of unknown coefficients and the Genocchi polynomials. Our main task is to compute the numerical values of the unknown coefficien...

This article is devoted to obtain the numerical solution for a class of nonlinear two-dimensional distributed-order time fractional diffusion equations. We discretize the problem by using a finite difference scheme in the time direction. Then, we solve the discretized nonlinear problem by a collocation approach based on the Legendre polynomials. Th...

The paper is concerned with the SIZR mathematical model for an outbreak of zombie infection with time-dependent infection rate. This class of the SIZR model involves equations that relate the susceptible S(t), the infected I(t), the zombie Z(t), and removed population R(t). The well poseness of the model is presented. The proposed model is then out...

The path of the Lévy process can be considered for prices of options such as a Rainbow or Basket option on two assets which leads to a 2D Black–Scholes model. The generalized model of this type of equation can be referred to as a 2D spatial-fractional Black–Scholes equation. The analytical solution of this kind is very complex and difficult and can...

Integro-differential equations are developed as models in enormous fields of engineering and science such as biological models, population growth, aerospace systems and industrial mathematics. In this work, we consider a general class of nonlinear fractional integro-differential equations with variable order derivative. We use the operational matri...

We provide a detailed description of a numerical approach that makes use of the shifted Chebyshev polynomials of the sixth kind to approximate the solution of some fractional order differential equations. Specifically, we choose the fractional Fisher–Kolmogorov–Petrovskii–Piskunov equation (FFKPPE) to describe this method. We write our approximate...

Providing effective numerical methods to approximate the solution of fractional order stochastic differential equations is of great importance, since the exact solution of this type of equations is not available in many cases. In this paper, a stepwise collocation method for solving a system of nonlinear stochastic fractional differential equations...

This paper presents a new method to solve the local fractional partial differential equations (LFPDEs) describing fractal vehicular traffic flow. Firstly, the existence and uniqueness of solutions to LFPDEs were proved and then two schemes known as the basic method (BM) and modified local fractional variational iteration method (LFVIM) were develop...

In this paper, a numerical algorithm is presented to obtain approximate solution of distributed order integro-differential equations. The approximate solution is expressed in the form of a polynomial with unknown coefficients and in place of differential and integral operators, we make use of matrices that we deduce from the shifted Legendre polyno...

In this paper, a new general double integral transform is introduced. We present its essential properties and proved some useful results such as the double convolution theorem and derivative properties. Furthermore, we apply the proposed double general integral transform to solve some partial differential equations such as telegraph and Klein–Gordo...

This paper presents a new method to solve the local fractional partial differential equations (LFPDEs) describing fractal vehicular traffic flow. Firstly, the existence and uniqueness of solutions to LFPDEs was proved and then two schemes known as the basic method (BM) and modified local fractional variational iteration method (LFVIM) were develope...

In this investigation, we propose a semi‐analytical technique to solve the fractional order Boussinesq equation (BsEq) that pertains the groundwater level in a gradient unconfined aquifer having an impervious extremity. With the aid of Antagana‐Baleanu fractional derivative operator and Laplace transform, several novel approximate‐analytical soluti...

In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To carry out the proposed scheme, we calculate the oper...

This work adopts to the time-fractional Klein–Gordon equation (FKGE) in the Caputo sense. We present a new technique using the clique polynomial as basis function for the operational matrices to obtain solution of time-FKGE. The key advantage of this technique is converting the time-FKGE to algebraic equations, which can be simply solved the proble...

In this article, a step-by-step collocation technique based on the Jacobi polynomials is considered to solve a class of neutral delay fractional stochastic differential equations (NDFSDEs). First, we convert the NDFSDE into a non-delay equation by applying a step-by-step method. Then, by using a Jacobi collocation technique in each step, a non-dela...

The usage of Lévy processes involving big moves or jumps over a short period of time has proven to be a successful strategy in financial analysis to capture such rare or extreme events of stock price dynamics.
Models that follow the Lévy process are FMLS, Kobol, and CGMY models. Such simulations steadily raise the attention of researchers...

The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore the applicability of this integral transform on Atangana–Baleanu derivative and the associated fractional integral. It is shown that by applying specific conditions on this integral transform, other integral transforms ar...

Solving linear system is central to scientific computations. Given a linear system Ax=b, where A is a non-singular real matrix. None of the existing solution approaches to the system is capable of exploiting special information provided by a proper sub-system. Only recently, Moradi et. al. (Nonlinear Dyn Syst Theory 19(1):193–199, 2019) showed that...

In this article, a step-by-step collocation approach based on the shifted Legendre polynomials is presented to solve a fractional order system of nonlinear stochastic differential equations involving a constant delay. The problem is considered with suitable initial condition and the fractional derivative is in the Caputo sense. With a step-by-step...

In this work, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To achieve to solution of this model, a numerical technique is in...

We investigated the analytical solution of fractional order K(m, n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we obtain the Lie point symmetries for this type of time-fractional partial differential equations (PDE). Also we pre...

In this paper, we solve the n-Generalized KdV equation by local fractional homotopy analysis method (LFHAM). Further, we analyze the approximate solution in the form of non-differentiable generalized functions defined on Cantor sets. Some examples and special cases of the main results are also discussed.

In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as a result reduction of the order and computing the conservation laws are presented. Furthermore, μ -symmetry and μ -conservation laws of the generalized Camassa–Holm equation are obtained.

In this article, the variational iteration method (VIM) is used to obtain approximate analytical solutions of the modified Camassa-Holm and Degasperis-Procesi equations. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials. The results reveal that the VIM...

In this research, the population dynamics model including the predator-prey problem and the logistic equation are generalized by using fractional operator in term of Caputo-Fabrizio derivative (CF-derivative). The models under study include of fractional Lotka-Volterra model (FLVM), fractional predator-prey model (FPPM) and fractional logistic mode...

In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana–Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier me...

Discrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks,
chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum
problems. First, we start with a novel discrete h-proportional fractional sum de�fined on the time
scale hZ so as to give the premise t...

In this paper, the Chebyshev spectral method is applied to solve the nonlinear Fisher fractional equation with initial boundary conditions. Here, the fractional derivative is considered in Caputo type. Then, using the Chebyshev spectral collocation method, the problem is transformed into an algebraic system. The results showed that this method is a...

In present work, a step-by-step Legendre collocation method is employed to solve a class of nonlinear fractional stochastic delay differential equations (FSDDEs). The step-by-step method converts the nonlinear FSDDE into a non-delay nonlinear fractional stochastic differential equation (FSDE). Then, a Legendre collocation approach is considered to...

In this article, a stochastic model is introduced to describe the spread of coronavirus with considering several disease compartments related to different age groups. The presented model is based on observing safety protocols, such as quarantine and mask use, by people at different ages. In order to simulate the natural randomness, some white noise...

The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform the problem into a continuous-time optimization problem and then utilize a transferred Legendre pseudospectral method to discretize the problem. By solving...

In this paper, we consider a pseudo‐parabolic equation with the Caputo fractional derivative. We study the existence and uniqueness of a class of mild solutions of these equations. For a nonlinear problem, we first investigate the global solution under the initial data u0 ∈ L². In the case of initial data u0 ∈ Lq, q ≠ 2, we obtain the local existen...

The differential transform method (DTM) in two dimensions just used for obtaining solution of those type of fractional partial differential equations (PDEs) which have solutions as separable functions i.e. w(x,t)=u(x)·v(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{a...