Abstract
This manuscript is devoted to obtain some adequate conditions for existence of at least one solution to fractional pantograph equation (FPE) involving the psi-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 stabilities for the considered problem. Our results are based on some standard fixed point theorems. For the demonstration of our results, we provide an example.