Some generalized numerical methods for solving higher-order of fractional partial differential equations with application

Abstract

This article recommends a computer method for solving some classes of higher-order fractional partial differential equations (FrPDEs). The updated techniques were made by combining the method of lines (MOL) and the numerical RK-type method. For solving certain types of FrPDEs that aren’t in the order, you might expect. Some problems with second-, third-, and fourth-order FrPDEs are solved with the methods made, and the numerical solutions are compared with the analytical answers. Also, a new type of application in classical physics called a wave FrPDE has been made for mechanical waves like water, earthquake, sound, and electromagnetic waves. Many examples are given to show how flexible and useful the method is. The numerical results are seen as the same as the exact solutions of the implementations to show how accurate and useful the suggested methods are. Also, the numerical implementations compare the suggested methods with exact solutions to show that they work and are accurate. The suggested methods used RKM analytical solutions to come up with numerical solutions to the test problems. Some examples are given to show how flexible and useful the method is. Also, the numerical implementations are compared with exact results to show that the proposed methods work and are accurate. R.K. techniques were used to find numerical answers to the suggested test problems.