Journal of Applied Science and Engineering

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Iman I. Gorial This email address is being protected from spambots. You need JavaScript enabled to view it.1

1Department of Materials Engineering, University of Technology, Iraq


Received: December 21, 2020
Accepted: May 10, 2021
Publication Date: June 30, 2021

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

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This paper presents an efficient approximation method for solving the Riesz space fractional percolation equation mixed fractional derivative (RSFPEMFD) with the initial condition (IC) and derivative boundary conditions (DBC) using explicit finite difference method (EFDM). The shifted Grunwald estimate was used for analysis of the mixed fractional derivatives. In addition, the analysis method of consistency, stability, and convergence was used for analyzing the EFDM. To demonstrate the efficiency and validity of the proposed algorithm, some illustrative examples are given and comparing results with the exact solution. The results are displayed when necessary in tables using the MathCAD and MATLAB software package. The EFDM for solving RSFPEMFD has been demonstrated to be effective and reliable.

Keywords: Explicit finite difference method (EFD), Fractional percolation equation (FPE), Riesz mixed fractional derivative, Stability, Convergence of numerical method


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