Caputo type modification of the Erdelyi-Kober fractional implicit differential equations with retarded and advanced arguments in Banach spaces

Abstract

This article deals with results concerning the existence of solutions for some functional implicit of Caputo type modification of the Erd\'elyi-Kober fractional differential equations, with both retarded and advanced arguments. The results are based on the M\"{o}nch’s and Darbo's fixed point theorem associated with the technique of measure of noncompactness, and we present an illustrative example.