Dynamics and stability of ψ-fractional pantograph equations with boundary conditions

Abstract

This manuscript is devoted to obtain some adequate conditions for existence of at least one solution to fractional pantograph equation (FPE) involving the ψ -fractional derivative. The proposed problem is studied under some boundary conditions. Since stability is an important aspect of the qualitative theory. Therefore, we also discuss the Ulam-Hyers and Ulam-Hyers-Rassias type stabilites for the considered problem. Our results are based on some standard fixed point theorems. For the demonstration of our results, we provide an example.