The Rishi Transform method for solving multi-high order fractional differential equations with constant coefficients

Abstract

In this paper, we suggest the Rishi transform, which may be used to find the analytic (exact) solution to multi-high-order linear fractional differential equations, where the Riemann-Liouville and Caputo fractional derivatives are used. We first developed the Rishi transform of foundational mathematical functions for this purpose and then described the important characteristics of the Rishi transform, which may be applied to solve ordinary differential equations and fractional differential equations. Following that, we found an exact solution to a particular example of fractional differential equations. We looked at four numerical problems and solved them all step by step to demonstrate the value of the Rishi transform. The results show that the suggested novel transform, "Rishi Transform, " yields exact solutions to multi-higher-order fractional differential equations without doing complicated calculation work.

Keywords

• linear fractional differential equations
• riemann-liouville's fractional derivative
• liouville-caputo's fractional derivative
• rishi transform
• inverse rishi transform