Integro-differential equations implicated with Caputo-Hadamard derivatives under nonlocal boundary constraints

Abstract

The goal of this work is to derive a new type of fractional system that arises from the
combination of the Caputo-Hadamard derivative with the integro-differential equation. Also,
the existence and uniqueness of solutions to this problem have been studied under nonlocal
boundary conditions. Moreover, Hyer-Ulam stability has been studied for the considered problem.
Finally, to reinforce the theoretical results and provide applications for our paper, two
supporting examples have been emphasized

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.…”