Solvability and Ulam–Hyers–Rassias stability for generalized sequential quantum fractional pantograph equations

Abstract

In the present manuscript, we discuss the existence, uniqueness an Ulam-stability of solutions for sequential fractional pantograph equations involving n Caputo and one Riemann–Liouville q−fractional derivatives. We prove the uniqueness of solutions for the given problem by using Banach’s contraction mapping principle. Then, the existence of at least one is obtained via Leray–Schauder’s alternative. Also, we define and study the Ulam-stability of solutions for the considered problem. Finally, an example is also given to point out the applicability of our main results.

Keywords

• Pantograph equation
• Fractional q–pantograph equation
• Fixed point
• Uniqueness
• Ulam–Hyers stability