Hossein Jafari

Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition

Adomian decomposition method has been used to obtain solutions of linear/nonlinear fractional diffusion and wave equations. Some illustrative examples have been presented.

Application of Legendre wavelets for solving fractional differential equations

In this paper, we develop a framework to obtain approximate numerical solutions to ordinary differential equations (ODEs) involving fractional order derivatives using Legendre wavelet approximations. The properties of Legendre wavelets are first presented. These properties are then utilized to reduce the fractional ordinary differential equations (FODEs) to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Results show that this technique can solve the linear and nonlinear fractional ordinary differential equations with negligible error compared to the exact solution.

REVISED ADOMIAN DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF NONLINEAR EQUATIONS

A modification of Adomian decomposition method is suggested and used for solving a system of nonlinear equations, which yields a series solution with accelerated convergence. Illustrative examples have been presented, to demonstrate the method and the results obtained are compared with those derived from the standard Adomian decomposition method.

Homotopy analysis method for solving multi-term linear and nonlinear diffusion–wave equations of fractional order

Abstract In this paper we have used the homotopy analysis method (HAM) to obtain solutions of multi-term linear and nonlinear diffusion–wave equations of fractional order. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented.

Application of the homotopy perturbation method to coupled system of partial differential equations with time fractional derivatives

The homotopy perturbation method (HPM) is applied to solve nonlinear partial differential equations of fractional orders. The corresponding solutions for integer orders of the fractional derivatives are found to be special cases of the fractional differential equations. It is predicted that HPM can be found widely applicable in engineering.

Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations

A modification of the Adomian decomposition method applied to systems of linear/nonlinear ordinary and fractional differential equations, which yields a series solution with accelerated convergence, has been presented. Illustrative examples have been given.

Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method

In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions.MSC:74H10, 35L05, 28A80.

Fractional complex transform method for wave equations on Cantor sets within local fractional differential operator

This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.

A new approach for solving a system of fractional partial differential equations

In this paper we propose a new method for solving systems of linear and nonlinear fractional partial differential equations. This method is a combination of the Laplace transform method and the Iterative method and here after called the Iterative Laplace transform method. This method gives solutions without any discretization and restrictive assumptions. The method is free from round-off errors and as a result the numerical computations are reduced. The fractional derivative is described in the Caputo sense. Finally, numerical examples are presented to illustrate the preciseness and effectiveness of the new technique.

The variational iteration method for solving n-th order fuzzy differential equations

The variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.