Existence and stability of solutions for fractional quantum hybrid pantograph problem

In this present work, we study a nonlinear fractional q-differential hybrid pantograph equation. We prove the uniqueness and estimate of solutions by means of Banach’s fixed point theorem and using the generalization of Gronwall’s inequality. We also study both Ulam-Hyers and the Ulam-Hyers-Rassias stabilities of mentioned problem. Finally, we give an illustrative example for our main results obtained in this paper