Proposed Method for Solving Quasi-Linear Fractional Partial Differential Equations Using α-Fractional Derivative

Abstract

The fractional partial differential equation (FPDE) plays a big role in engineering and applied science. Finding the solutions to the FPDEs is a significant subject and a wide field. The objective of this article is to use the α-fractional derivative definition for converting the FPDE to a partial differential equation (PDE) and then, we use the method of lines for solving a quasi-linear PDE. The characteristic of the α-fractional derivative definition is appropriate, significant, and powerful. Additionally, the properties of the definition ofα-fractional derivative are used for converting the quasi-linear (FPDE) to a PDE. Hence, the PDE is converted to a system of ordinary differential equations(ODEs) by using the method of lines (MOL). Some implementations are solved using the proposed method and then, compared with exact or numerical solutions. The test implementations showed that the proposed method agrees well with their solutions. Hence, the algorithm of this method proved to be efficient and accurate.