Hilfer fractional quantum system with Riemann-Liouville fractional derivatives and integrals in boundary conditions

Abstract

In this paper, we initiate the study of existence and uniqueness of solutions for a coupled system involving Hilfer fractional quantum derivatives with nonlocal boundary value conditions containing $ q $-Riemann-Liouville fractional derivatives and integrals. Our results are supported by some well-known fixed-point theories, including the Banach contraction mapping principle, Leray-Schauder alternative and the Krasnosel'skiǐ fixed-point theorem. Examples of these systems are also given in the end.

Keywords

• quantum calculus
• hilfer derivative
• systems
• existence and uniqueness