Generalized RKM methods for solving fifth-order quasi-linear fractional partial differential equation

Abstract

Fractional differential equations (FDEs) are used for modeling the natural phenomena and interpretation of many life problems in the fields of applied science and engineering. The mathematical models which include different types of differential equations are used in some fields of applied sciences like biology, diffusion, electronic circuits, damping laws, fluid mechanics, and many others. The derivation of modern analytical or numerical methods for solving FDEs is a significant problem. However, in this article, we introduce a novel approach to generalize Runge Kutta Mechee (RKM) method for solving a class of fifth-order fractional partial differential equations (FPDEs) by combining numerical RKM techniques with the method of lines. We have applied the developed approach to solve some problems involving fifth-order FPDEs, and then, the numerical and analytical solutions for these problems have been compared. The comparisons in the implementations have proved the efficiency and accuracy of the developed RKM method.