On pantograph multi-point boundary value problem with Caputo $q$-fractional derivative


Houari Bouzid, Abdelkader Benali, Abdelkrim Salim




The purpose of this research is to investigate the existence and uniqueness of several solutions to the multi-point boundary value problem of nonlinear fractional differential equations involving two fractional derivatives. We demonstrate the existence of solutions by applying a number of fixed point theorems, including Banach’s fixed point theorem, nonlinear alternative of Leray-Schauder type, and Leray-Schauder degree. Finally, two examples are presented to demonstrate our results.