Green's functions for boundary value problems of generalized fractional differential equations with p-Laplacian

Abstract

We utilize the recently presented generalized fractional derivatives, which are not the same as standard Caputo and Riemann-Liouville fractional derivatives, to reformulate some boundary value problems of fractional differential equations. For some classes of generalized fractional differential equations with boundary conditions build up, we find the corresponding Green's functions and establish their properties under suitable assumptions and we also demonstrate the applicability of these properties of the Green's functions to establish some existence results via fixed point theorems.