Papers by Prof. Hossein Jafari
In this paper, we present a new modification of Adomian decomposition method (ADM) for finding ex... more In this paper, we present a new modification of Adomian decomposition method (ADM) for finding exact solutions of nonlinear integral equations. In [Appl. Math. Comput. 170 (2005) 570-583], the author introduced a modification of ADM, namely two step Adomian decomposition method (TSADM) that facilitates the calculations. However, there is a weakness in TSADM which we invistigate in this paper. We propose a new reliable modification of the ADM and apply this new modified method to solve the Volterra and Fredholm integral equations. Some examples are given to illustrate the ability and reliability of this new modified method. The results reveal that our modified method is very simple and effective. MSC: 45B05 • 45D05• 49M27
In this paper we discuss the efficiency of the sub-equation method to construct the exact analyti... more In this paper we discuss the efficiency of the sub-equation method to construct the exact analytical solutions of the nonlinear time-fractional equations. The fractional sub-equation method is considered for application to the space-time fractional Telegraph and Burgers-Huxley equations. These solutions include the generalized trigonometric function solutions, generalized hyperbolic function solutions, and rational function solutions, which they are benefit to further understand the concepts of the complicated nonlinear physical phenomena and fractional differential equations. In this work we use of Mathematica for computations and programming. MSC: 34Kxx • 34K37
In this paper, a direct method for numerical solution of linear Fredholm integral equations syste... more In this paper, a direct method for numerical solution of linear Fredholm integral equations system by using Legendre wavelets is presented. Another method for solving Volterra type system of linear integral equations which uses zeros of Legendre wavelets for collocation points is introduced and used to reduce this type of system of integral equations to a system of algebraic equations.
In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. ... more In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-wovens and filtration industries. By using operational matrix of integration and multiplication the investigated equations are turned into set of algebraic equations. Numerical solutions show both accuracy and simplicity of the suggested approach.
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. is implemented to obtain MSC: 35R11 • 74H10
In this paper a numerical method for solving a class of fractional optimal control problems is pr... more In this paper a numerical method for solving a class of fractional optimal control problems is presented which is based on Bernstein polynomials approximation. Operational matrices of integration, differentiation, dual and product are introduced and are utilized to reduce the problem of solving a system of algebraic equations. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
This article presents the approximate analytical solutions of first order linear partial differen... more This article presents the approximate analytical solutions of first order linear partial differential equations (PDEs) with fractional time- and space- derivatives. With the aid of initial values, the explicit solutions of the equations are solved making use of reliable algorithm like homotopy analysis method (HAM). The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described in Caputo sense. Numerical results show that the HAM is easy to implement and accurate when applied to space- time- fractional PDEs.
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.
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.
In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called D... more In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.
In this paper, we present an efficient modification of the homotopy analysis method (HAM) that wi... more In this paper, we present an efficient modification of the homotopy analysis method (HAM) that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy analysis method. This modification of the homotopy analysis method is applied to nonlinear integral equations and mixed Volterra-Fredholm integral equations, which yields a series solution with accelerated convergence. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work.
In this paper, the variational iteration method (VIM) is employed to obtain approximate analytica... more In this paper, the variational iteration method (VIM) is employed to obtain approximate analytical solutions of the Stefan problem. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials.
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.
Finance is one of the fastest developing areas in the modern banking and corporate world. In this... more Finance is one of the fastest developing areas in the modern banking and corporate world. In this paper, we apply the Reduced Differential Transform Method (RDTM) for solving Black-Scholese equation for European option valuation. The same algorithm can be used for European put option. The results show that this method is very effective and simple. MSC: 35C10 † 74G10
In this article, the local fractional variational iteration method is proposed to solve nonlinear... more In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the proposed method is capable of solving effectively a large number of nonlinear differential equations with high accuracy. In addition, we show that local fractional 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 engineering and physics.
In this paper we discuss the efficiency of the sub-equation method to construct the exact analyti... more In this paper we discuss the efficiency of the sub-equation method to construct the exact analytical solutions of the nonlinear time-fractional equations. The fractional sub-equation method is considered for application to the spacetime fractional Telegraph and Burgers-Huxley equations. These solutions include the generalized trigonometric function solutions, generalized hyperbolic function solutions, and rational function solutions, which they are benefit to further understand the concepts of the complicated nonlinear physical phenomena and fractional differential equations. In this work we use of Mathematica for computations and programming. MSC: 34Kxx • 34K37
In this paper, we consider a particle with spin 1 2 in de Sitter space-time. Procedure for transi... more In this paper, we consider a particle with spin 1 2 in de Sitter space-time. Procedure for transition to the Pauli approximation is conducted in the equation in the variable (t, r), obtained after separating the angular dependence of (θ, φ) from the wave function. We make the suitable second order equation corresponding to de Sitter space time for particle spine 12 we then compare this equation to Jacobi polynomial and obtain the wave function and eigenvalues (energy spectrum) which is important for the corresponding system. Also, by taking the advantage from weight and main function in Jacobi polynomial and obtain the corresponding algebra.
In this paper, the simplest equation method has been used for finding the general exact solutions... more In this paper, the simplest equation method has been used for finding the general exact solutions of nonlinear evolution equations that namely (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff( CBS) equation and (2+1)-dimensional breaking soliton equation (BS) when the simplest equation is the equation of Riccati
Pramana
The purpose of this paper is to suggest a numerical technique to solve fractional variational pro... more 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 Bernstein polynomials. By this method, a system of algebraic equations is driven. We provide examples to show the effectiveness of this technique, which is considered in the current study.
Chaos, Solitons & Fractals
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Papers by Prof. Hossein Jafari