In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

We make the split of integral fractional Laplacian as $(-\Delta)^s u=(-\Delta)(-\Delta)^{s-1}u$, where $s\in(0,\frac{1}{2})\cup(\frac{1}{2},1)$. Based on this splitting, we respectively discretize one- and two-dimensional with inhomogeneous Dirichlet boundary condition give corresponding truncation errors help interpolation estimate. Moreover, suitable corrections are proposed to guarantee conv...

in this paper, the temperature distribution around a moving heat source had been investigated including the phase change and non phase change . in non-phase change state, the governing equation was converted to finite difference equation by finite volume method and the equation was solved by alternating direction implicit method. this method was unconditionally stable . in phase change state, t...

Abstract Heat transfer in skin tissue is an area of interest for medical sciences. In this paper we intend to study fractional bioheat equation for heat transfer in skin tissue with constant and sinusoidal heat flux condition on skin surface. Numerical solutions are obtained by implicit finite difference method. We study the effect of anomalous diffusion in skin tissue and compare it with norma...

In this paper, we develop the Crank-Nicolson finite difference method (C-N-FDM) to solve the linear time-fractional diffusion equation, formulated with Caputo’s fractional derivative. Special attention is given to study the stability of the proposed method which is introduced by means of a recently proposed procedure akin to the standard Von-Neumann stable analysis. Some numerical examples are ...

In this article, numerical study for the fractional Cable equation which is fundamental equations for modeling neuronal dynamics is introduced by using weighted average of finite difference methods. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. A simple and an accurate stability criterion val...

Abstract This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of two-dimensional time-fractional Sobolev equation. The model is formulated with Caputo fractional derivative. uses RBF approximate spatial operator, and finite-difference algorithm as time-stepping approach for in time. stability technique examined by using matrix method. Finally, two numer...