On the nonlocal hybrid (k,φ)-Hilfer inverse problem with delay and anticipation

Abstract

This paper focused on establishing results regarding the existence of solutions for a class of nonlocal terminal value problems involving hybrid implicit nonlinear fractional differential equations with the $ ({\mathsf{k}}, {\rm{\mathsf{φ}}}) $-Hilfer fractional derivative, which includes both finite delay and anticipation arguments. Our analysis was based on the Banach fixed point technique, and the Schauder and Krasnoselskii fixed point theorems. Moreover, illustrative examples were considered to support our new results.

Keywords

• $ ({\mathsf{k}}
• {\rm{\mathsf{φ}}}) $-hilfer fractional derivative
• hybrid equations
• terminal value problem
• retarded arguments
• advanced arguments
• existence
• uniqueness
• nonlocal condition