A Novel Numerical Method for a Class of Hattaf Fractional Differential Equations

Abstract

Fractional operators of differentiation and integration have become essential tools for modeling a wide range of phenomena encountered in science, industry and engineering. This paper presents a direct numerical scheme for fractional differential equations involving the generalized Hattaf fractional (GHF) derivative, avoiding the common approach of converting these equations into integral forms. In addition, a comprehensive theoretical analysis of the scheme’s consistency, stability and convergence is provided. Furthermore, the inclusion of both purely mathematical examples and an application to an economic model highlights the practical relevance of the proposed method.