A multi-step formable transform decomposition method for solving fractional order Riccati equation

Abstract

A multi-step formable transform decomposition method (MFTDM) is suggested in this study to solve the nonlinear fractional-order Riccati problem. It is well understood that a corresponding numerical solution given by the FTDM is only valid for a short period of time. In the case of integer-order systems, however, the MFTDM solutions are more correct and reliable throughout time and are in very good agreement with the exact solutions. The fractional derivative is described in the Caputo sense. The method is tested on prominent examples, and the results show that it is accurate and efficient when compared to other numerical methods.