A novel numerical manner for two‐dimensional space fractional diffusion equation arising in transport phenomena

Abstract

Fractional diffusion equations include a consistent and efficient explanation of transport phenomena that manifest abnormal diffusion, that cannot be often represented by second‐order diffusion equations. In this article, a two‐dimensional space fractional diffusion equation (SFDE‐2D) with nonhomogeneous and homogeneous boundary conditions is considered in Caputo derivative sense. An instant and nevertheless accurate scheme is obtained by the finite‐difference discretization to get the semidiscrete in temporal derivative with convergence order Ofalse(δτ2false). Moreover, space fractional derivative can be approximated based on the Chebyshev polynomials of second kind which are powerful methods for basing the operational matrix. The convergence and stability of the proposed scheme are discussed theoretically in detail. Finally, two numerical problems with an exact solution are given that numerical results show the effectiveness of the new techniques. These schemes can be simply extended to three spatial dimensions, which will be the subject of our subsequent research.

Numerical approach to simulate diffusion model of a fluid-flow in a porous media

“…( 4), we need to have the closed form of the fractional derivative of the ,  order for basis polynomials. This form is obtained in the paper [13]:…”

Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term

“…Partial differential equations (PDEs) have applications in many branches of science and engineering; see for example [1][2][3][4][5][6][7][8]. In this paper, for s > 1, we consider the initial value problem for the conformable heat equation (or called parabolic equation with conformable operator)…”

Stability of a nonlinear fractional pseudo-parabolic equation system regarding fractional order of the time

“…In addition, there are numerous works on the well-posedness of the pseudo-parabolic equation with classical derivative, as evidenced by [60][61][62][63][64][65][66][67][68] and the references therein. Investigating the existence, uniqueness, and stability of fractional differential equations, has been the important goal in the scientific community, especially in fractional calculus.…”