An analytical solution for the Caputo type generalized fractional evolution equation

Abstract

The Caputo type generalized fractional evolution equation is studied in this paper. Since the Caputo type generalized fractional derivative is well-known for being the generalization of Caputo fractional derivatives, this article’s studies contribute to the solving of a variety of fractional differential equations in the sense of Caputo type generalized fractional derivative and Caputo fractional derivative. Moreover, the fractional Green’s functions for those fractional differential equations are obtained. The generalized Laplace transform and generalized Mellin transform are used to effectively and successfully achieve the desired results. Importantly, the generalized Mellin transform is firstly proposed here.

Keywords

• Fractional evolution equations
• Caputo type generalized fractional derivative
• Fractional Green’s functions
• Generalized Mellin transform
• Generalized Laplace transform