Hossein Jafari

Hossein Jafari
University of Mazandaran | UMZ

Professor

About

306
Publications
92,494
Reads
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7,712
Citations
Additional affiliations
December 2006 - December 2010
University of Mazandaran
Position
  • Professor (Associate)
June 2003 - December 2006
Savitribai Phule Pune University
Position
  • PhD Student
Education
June 2003 - December 2006
Savitribai Phule Pune University
Field of study
  • Applied Mathematics
September 1998 - January 2001
Tarbiat Modares University
Field of study
  • Applied Mathematics
September 1994 - June 1998
University of Mazandaran
Field of study
  • Mathematics

Publications

Publications (306)
Article
Full-text available
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...
Article
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...
Article
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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...
Article
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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...
Article
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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...
Article
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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...
Article
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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...
Article
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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...
Article
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...
Article
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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...
Article
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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...
Article
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...
Article
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...
Article
Full-text available
‎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...
Article
Full-text available
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...
Article
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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...
Article
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...
Article
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...
Chapter
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...
Article
Full-text available
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.
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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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...
Article
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...
Article
Full-text available
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...
Article
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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...
Article
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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...
Article
This paper is associated to investigate a stochastic SEIAQHR model for transmission of Coronavirus disease 2019 that is a recent great crisis in numerous societies. This stochastic pandemic model is established due to several safety protocols, for instance social-distancing, mask use and quarantine. Three white noises are added to three of the main...
Article
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In this paper, we solve the [Formula: see text]-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.
Article
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In this paper, we utilize local fractional reduced differential transform (LFRDTM) and local fractional Laplace variational iteration methods (LFLVIM) to obtain approximate solutions for coupled KdV equations. The obtained results by both presented methods (the LFRDTM and the LFLVIM) are compared together. The results clearly show that those sugges...
Article
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When a particle distributes at a rate that deviates from the classical Brownian motion model, fractional space derivatives have been used to simulate anomalous diffusion or dispersion. When a fractional derivative substitutes the second-order derivative in a diffusion or dispersion model, amplified diffusion occurs (named super-diffusion). The prop...
Article
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Lie symmetry analysis is achieved on a new system of coupled KdV equations with fractional order, which arise in the analysis of several problems in theoretical physics and numerous scientific phenomena. We determine the reduced fractional ODE system corresponding to the governing factional PDE system. In addition, we develop the conservation laws...
Article
In recent years, a new definition of fractional derivative which has a nonlocal and non-singular kernel has been proposed by Atangana and Baleanu. This new definition is called the Atangana-Baleanu derivative. In this paper, we present a new technique to obtain the numerical solution of advection-diffusion equation containing Atangana-Baleanu deriv...
Article
In this study, we propose a mathematical model about the spread of novel coronavirus. This model is a system of fractional order differential equations in Caputo’s sense. The aim is to explain the virus transmission and to investigate the impact of quarantine on decreasing the prevalence rate of the virus in the environment. The unique solvability...
Article
Full-text available
In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions h...
Article
Fractional diffusion equations include a consistent and efficient explanation of transport phenomena that manifest abnormal diffusion, that can not be often represented by second-order diffusion equations.‎ ‎In this paper, a two-dimensional space fractional diffusion equation (SFDE-2D) with nonhomogeneous and homogeneous boundary conditions is con...
Article
The purpose of this paper is to suggest a numerical technique to solve fractional variational problems (FVPs). These problems are based on Caputo fractional derivatives. Rayleigh–Ritz method is used in this technique. First we approximate the objective function by the trapezoidal rule. Then, the unknown function is expanded in terms of the Bernstei...
Article
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The manuscript details a numerical method for solving a system of fractional differential equations (SFDEs) based on the Caputo fractional derivative by the Ritz method. To use this method, we transform the SFDEs into an optimization problem and obtain the system of nonlinear algebraic equations. Using polynomials of basis functions, we approximate...
Article
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This paper investigates the role of fractional calculus in data fitting. We show that while the Caputo and Atangana-Baleanu fractional derivatives can be applied successfully in data fitting, this might not be true for the conformable derivative. The conformable derivative results in an unnecessarily complicated differential equation that warrants...
Article
In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre p...
Article
Full-text available
In this work, a general class of pantograph type nonlinear fractional integro-differential equations (PT-FIDEs) with non-singular and non-local kernel is considered. A numerical scheme based on the orthogonal basis functions including the shifted Legendre polynomials (SLPs) is proposed. First, we expand the unknown function and its derivatives in t...
Article
Full-text available
Introduction: Integral transforms are important to solve real problems. Appropriate choice of integral transforms helps to convert differential equations as well as integral equations into terms of an algebraic equation that can be solved easily.During last two decades many integral transforms in the class of Laplace transform are introduced such...
Article
Full-text available
The theory of real quaternion differential equations has several applications through physics and engineering. In the present investigation, a decomposition method which is well known as the Adomian decomposition method is used to solve the linear quaternion differential equations. The obtained results show the applicability and usefulness of the A...
Article
Full-text available
This paper develops a numerical scheme for finding the approximate solution of space fractional order of the diffusion equation (SFODE). Firstly, the compact finite difference (CFD) with convergence order O(δτ^2) is used for discretizing time derivative. Afterward, the spatial fractional derivative is approximated by the Chebyshev collocation metho...
Preprint
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 pres...
Article
Full-text available
A spectral collocation approach is constructed to solve a class of time-fractional stochastic heat equations (TFSHEs) driven by Brownian motion. Stochastic differential equations with additive noise have an important role in explaining some symmetry phenomena such as symmetry breaking in molecular vibrations. Finding the exact solution of such equa...
Article
Full-text available
This paper develops the solution of the two-dimensional time fractional evolution model using finite difference scheme derived from radial basis function (RBF-FD) method. In this discretization process, a finite difference formula is implemented to discrete the temporal variable, while the local RBF-FD formulation is utilized to approximate the spa...
Article
Full-text available
This paper deals with approximating the time fractional Tricomi-type model in the sense of the Caputo derivative. The model is often adopted for describing the anomalous process of nearly sonic speed gas dynamics. The temporal semi-discretization is computed via finite difference algorithm, while the spatial discretization is obtained using the loc...
Article
In this study, we examine the interaction between drug addiction and the contagion of HIV/AIDS in Iranian prisons. We provide a simple mathematical model for such an interaction. The stability of drug addiction and HIV/AIDS models are analyzed separately with no medical treatment. Then, we present an improved model describing the effect of treatmen...
Book
Full-text available
To Mathematician around the world, all of us know well that mathematics is the mother of all other sciences and all of us know well that no progress without progress of the mother of all sciences. Also all of us know that all of us will die and the work will still alive. Our main message herein, is to respect the mathematics, especially in all Arab...
Article
In this paper, a sixth-kind Chebyshev collocation method will be considered for solving a class of variable order fractional nonlinear quadratic integro-differential equations (V-OFNQIDEs). The operational matrix of variable order fractional derivative for sixth-kind Chebyshev polynomials is derived and then, a collocation approach is employed to r...
Article
In this work, we consider a class of nonlinear integro-differential equations of variable-order. Existence, uniqueness and stability results are discussed. For solving the considered equations, operational matrices based on the shifted Legendre polynomials are used. First, we approximate the unknown function and its derivatives in terms of the shif...
Book
Full-text available
To Mathematician around the world, all of us know well that mathematics is the mother of all other sciences and all of us know well that no progress without progress of the mother of all sciences. Also all of us know that all of us will die and the work will still alive. Our main message herein, is to respect the mathematics, especially in all Arab...
Article
Recently, Atangana and Baleanu have defined a new fractional derivative which has a nonlocal and non-singular kernel. It is called the Atangana–Baleanu derivative. In this paper we present a numerical technique to obtain solution of fractional differential equations containing Atangana–Baleanu derivative. For this purpose, we use the operational ma...
Article
Full-text available
Consider the first-order linear differential equation with several retarded arguments(Formula Presented), where the functions (Formula Presented). New oscillation criteria which essentially improve known results in the literature are established.An example illustrating the results is given.
Article
In this work, we consider a general class of nonlinear Volterra integro-differential equations with Atangana–Baleanu derivative. We use the operational matrices based on the shifted Legendre polynomials to obtain numerical solution of the considered equations. By approxi-mating the unknown function and its derivative in terms of the shifted Legendr...
Article
Full-text available
In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions h...
Article
Full-text available
The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caput...
Article
Full-text available
The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caput...
Research Proposal
Full-text available
About this Research Topic Synchronization describes the linking of two chaotic systems with a common signal or signals, the trajectories of one of the systems will converge to the same values as the other and they will remain in step with each other. When this occurs, the synchronization is said to be structurally stable. The idea of synchronizatio...