The existence, uniqueness, and stability results for a nonlinear coupled system using ψ-Caputo fractional derivatives

Abstract

Abstract In this article, we use coupled boundary conditions on a nonlinear system with ψ-Caputo fractional derivatives to derive new conclusions on the solution’s existence, uniqueness, and stability. We use the well-known tools of fixed-point theory to establish the proposed results. We give an example to verify the theoretical findings. The proposed existence, uniqueness, and stability analyses considering the ψ-Caputo fractional derivative are the novelty of this article.

Keywords

• ψ-Caputo derivative
• Fractional boundary value problem
• Existence and uniqueness
• Hyers–Ulam stability