On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions

Abstract

We investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the existence of this fractional BVP and its unique solution. The boundary conditions (BCs) established in this study are of a more general type and can be reduced to numerous specific examples by defining the parameters involved in the conditions. In this way, we extend some recent nice results. At the end, we use an example to verify our results.

Keywords

• impulsive
• integro-differential equations
• Caputo–Hadamard fractional derivative
• boundary value problems