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Hossein Jafari

University of Mazandaran, Mathematics, Faculty Member

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Papers by Hossein Jafari

$Research paper thumbnail of Analysis of fractional Navier–Stokes equations$

Analysis of fractional Navier–Stokes equations

Heat Transfer

In this study, we apply the fractional Laplace variational iteration method (FLVIM), a computer m... more 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 by the suggested method. In addition, the fractional Laplace variational iteration method solution's error analysis is covered. The computational technique also clearly demonstrates the validity and dependability of the suggested method for solving fractional Navier‐Stokes equations. Furthermore, the obtained solutions are a perfect fit with previously established solutions.

A New Approach for Solving System of Local Fractional Partial Differential Equations

In this paper, we apply a new method for solving system of partial differential equations within ... more In this paper, we apply a new method for solving system of partial differential equations within local fractional derivative operators. The approximate analytical solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm. The obtained results show that the introduced approach is a promising tool for solving system of linear and nonlinear local fractional differential equations. Furthermore, we show that local fractional Laplace variational iteration method is able to solve a large class of nonlinear problems involving local fractional operators effectively, more easily and accurately; and thus it has been widely applicable in physics and engineering.

Local Fractional Adomain Decomposition Method for Solving Two Dimensional Heat conduction Equations within Local Fractional Operators

Journal of Advances in Mathematics, 2014

In this paper, the two-dimensional heat conduction equations with local fractionalderivative oper... more In this paper, the two-dimensional heat conduction equations with local fractionalderivative operators are investigated. Analytical solutions are obtained by using the localfractional Adomian decomposition method. The results obtained show that the numericalmethod based on the proposed technique gives us the exact solution Illustrative examples areincluded to demonstrate the validity and applicability of the new technique.

Lie Group Theory for Nonlinear Fractional K(m, n) Type Equation with Variable Coefficients

Studies in Systems, Decision and Control, 2021

We investigated the analytical solution of fractional order K(m,n) type equation with variable co... more 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 timefractional partial differential equations (PDE). Also we present the corresponding reduced fractional differential equations (FDEs) corresponding to the time-fractional K(m,n) type equation.

$Research paper thumbnail of Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order$

Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order

Open Physics, 2016

The fractional Burgers equation describes the physical processes of unidirectional propagation of... more The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.

Approximate Solution for Nonlinear Gas Dynamic and Coupled KdV Equations Involving Local Fractional Operator

Journal of Zankoy Sulaimani - Part A, 2015

$Research paper thumbnail of Application of the Local fractional Adomian Decomposition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets$

Application of the Local fractional Adomian Decomposition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets

Journal of Zankoy Sulaimani - Part A, 2015

In this paper, we will compare between the local fractional Adomian decomposition method (LFADM) ... more In this paper, we will compare between the local fractional Adomian decomposition method (LFADM) and local fractional series expansion method (LFSEM) for solving the telegraph equation on Cantor sets within local fractional operator. The results obtained by (LFADM) are compared with the results obtained by (LFSEM). Some examples are given to illustrate the efficiency and accuracy of the presented methods.

$Research paper thumbnail of Group classification of the time-fractional Kaup-Kupershmidt equation$

Group classification of the time-fractional Kaup-Kupershmidt equation

Scientia Iranica, 2017

Finding the symmetries of the nonlinear fractional di erential equations plays an important role ... more Finding the symmetries of the nonlinear fractional di erential equations plays an important role in study of fractional di erential equations. In this manuscript, rstly, we are interested in nding the Lie point symmetries of the time-fractional Kaup-Kupershmidt equation. Afterwards, by using the in nitesimal generators, we determine their corresponding invariant solutions.

A Decomposition Method for Solving the Fractional Davey-Stewartson Equations

International Journal of Applied and Computational Mathematics, 2015

In the present paper, we apply the new iterative method which proposed by Daftardar-Gejji and Jaf... more In the present paper, we apply the new iterative method which proposed by Daftardar-Gejji and Jafari to solve fractional Davey-Stewartson equations. The convergence of this method is proved. The results obtained by this method have been compared with the exact solutions and show that proposed method is accuracy and convenience for solving nonlinear fractional differential equations.

$Research paper thumbnail of Numerical solutions of multi-order fractional differential equations by Boubaker polynomials$

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

Open Physics, 2016

In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approxi... more In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations

Entropy, 2016

In this manuscript, we prove the existence and uniqueness of solutions for local fractional diffe... more In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results.

On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

Entropy, 2016

In this paper, we consider the local fractional decomposition method, variational iteration metho... more In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

$Research paper thumbnail of A decomposition method for solving diffusion equations via local fractional time derivative$

A decomposition method for solving diffusion equations via local fractional time derivative

Thermal Science, 2015

In this paper a decomposition method based on Daftardar-Jafari method is applied for solving diff... more

$Research paper thumbnail of Numerical solutions of telegraph and Laplace equations on Cantor sets using local fractional Laplace decomposition method$

Numerical solutions of telegraph and Laplace equations on Cantor sets using local fractional Laplace decomposition method

In this paper, the local fractional Laplace decomposition method is implemented to obtain approxi... more In this paper, the local fractional Laplace decomposition method is implemented to obtain approximate analytical solution of the telegraph and Laplace equations on Cantor sets. This method is a combination of the Yang-Laplace transform and the Adomian decomposition method. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

$Research paper thumbnail of Fractional Lie group method of the time-fractional Boussinesq equation$

Fractional Lie group method of the time-fractional Boussinesq equation

Nonlinear Dynamics, 2015

Finding the symmetries of the nonlinear fractional differential equations is a topic which has ma... more Finding the symmetries of the nonlinear fractional differential equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.

Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators

Advances in Mathematical Physics, 2014

We perform a comparison between the local fractional Adomian decomposition and local fractional f... more We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Solutions of the Fractional Davey-Stewartson Equations with Variational Iteration Method

Rom. Rep. Phys, 2012

This paper presents approximate analytical solutions for the fractional Davey-Stewartson equation... more This paper presents approximate analytical solutions for the fractional Davey-Stewartson equations using the Variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. The results obtained by this method have been compared with the exact solutions and show that the introduced approach is a promising tool for solving many linear and nonlinear fractional differential equations.

Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations

Abstract and Applied Analysis, 2013

The fractional subequation method is applied to solve Cahn-Hilliard and Klein-Gordon equations of... more

The Name of the Game

In the past centuries, there was no problem or fault in misleading names for same definitions or ... more In the past centuries, there was no problem or fault in misleading names for same definitions or similar methods due to lack of access to information such as journals and internet. Unfortunately, one of the serious challenges in Mathematics is the originality of the new definitions and methods presented in recent decades. With a little research and accuracy in some of them, it can be shown that some of these definitions and methods are not new. I will illustrate in this talk that there are similarities to the classical methods or some other exiting methods. ∗Email: jafarh@unisa.ac.za, jafari.usern@gmail.com 1

Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative

Abstract and Applied Analysis, 2014

The Fourier law of one-dimensional heat conduction equation in fractal media is investigated in t... more The Fourier law of one-dimensional heat conduction equation in fractal media is investigated in this paper. An approximate solution to one-dimensional local fractional Volterra integral equation of the second kind, which is derived from the transformation of Fourier flux equation in discontinuous media, is considered. The Picard successive approximation method is applied to solve the temperature field based on the given Mittag-Leffler-type Fourier flux distribution in fractal media. The nondifferential approximate solutions are given to show the efficiency of the present method.