Solvability and stability for a fractional quantum jerk type problem including Riemann–Liouville-Caputo fractional q−derivatives

Abstract

This manuscript studies the existence and Ulam–Hyers stability results of solutions of q−fractional jerk type problem. The uniqueness of solutions is established by means of Banach’s contraction mapping principle, while the existence of solutions is derived from Leray–Schauder’s alternative. Also the stability in the sense of Ulam–Hyers stability is defined and studied. In conclusion, we display an case to appear the pertinence of the most comes about.

Keywords

• Fractional q−difference equations
• Fractional jerk equation
• Existence
• Nonlinear analysis
• Ulam–Hyers stability