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.

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

“…For more details on Hadamard fractional calculus, we refer the reader to [2][3][4][5][6] and the references therein. In recent years, the study of Hadamard fractional differential equations has attracted the attention of many scholars, mainly focusing on the existence, stability and approximation of solutions (see [7][8][9][10][11][12][13][14][15][16][17][18][19]). For example, Huang et al [9] applied a nonlinear alternative of Leray-Schauder to study the existence of solutions to a nonlinear coupled Hadamard fractional system.…”