Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses

Abstract

Abstract In this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and δ − d e r i v a t i v e $\delta -derivative$ initial conditions. By employing Banach’s and Schaefer’s fixed-point theorems, we attain the required results. Finally, we provide examples that support the main findings we arrived at.

Keywords

• Caputo–Hadamard derivative
• Noninstantaneous impulses
• Existence and uniqueness
• Ulam–Hyers stability