Generalized numerical RKM method for solving sixth-order fractional partial differential equations

Abstract Fractional partial differential equations (FPDEs) are used as tools in the mathematical modeling of the natural phenomena and interpretation of many life problems in the fields of engineering and applied science. Mathematical models that include different types of partial differential equations are used in some fields of applied sciences such as biology, diffusion, electronic circuits, damping laws, and fluid mechanics. The derivation of modern analytical or numerical methods for solving FPDEs is a significant problem. In this article an efficient numerical method is proposed for solving a class of sixth-order FPDEs in which created by combining numerical Runge–Kutta–Mohammed (RKM) techniques with the method of lines. We have applied the modified approach to solve some problems involving the sixth-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. Also, the wave equation of fractional order as an application of the wave equation has been presented. Additionally, by contrasting the numerical implementations with exact answers, the effectiveness and accuracy of the suggested methodologies are shown.