Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs

Abstract

The purpose of this work is to develop a semi-analytical numerical scheme for solving fractional order non-linear partial differential equations (FOPDEs), particularly inhomogeneous FOPDEs, expressed in terms of the Caputo-Fabrizio fractional order derivative operator. To achieve this goal, we examine several fractional versions of nonlinear model equations from the literature. We then present the proposed scheme, discussing its stability and convergence properties. We show that the proposed scheme is efficient and accurate, and we provide numerical examples to illustrate its performance. Our findings demonstrate that the scheme has significant potential for solving a wide range of complex FOPDEs. Overall, this work contributes to the advancement of numerical techniques for solving fractional order non-linear partial differential equations and lays a foundation for further research in this area.