Application of fractional quantum calculus on coupled hybrid differential systems within the sequential Caputo fractional q-derivatives

Abstract

In the current manuscript, we combine the q-fractional integral operator and q-fractional derivative to investigate a coupled hybrid fractional q-differential systems with sequential fractional q-derivatives. The existence and uniqueness of solutions for the proposed system are established by means of Leray-Schauder’s alternative and the Banach contraction principle. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability results are discussed. Finally, two illustrative examples are given to highlight the theoretical findings.

Keywords

• fractional q-calculus
• existence and uniqueness of solutions
• boundary conditions
• ulam-hyers-stability
• fixed point
• 26a33
• 34a08
• 34a12