On a fractional Caputo–Hadamard problem with boundary value conditions via different orders of the Hadamard fractional operators

[摘要] We investigate the existence of solutions for a Caputo–Hadamard fractional integro-differential equation with boundary value conditions involving the Hadamard fractional operators via different orders. By using the Krasnoselskii’s fixed point theorem, the Leray–Schauder nonlinear alternative, and the Banach contraction principle, we prove our main results. Also, we provide three examples to illustrate our main results.

[学科分类] 航空航天科学

[关键词] Boundary value problem;Leray–Schauder;The Caputo–Hadamard fractional derivative;The Hadamard fractional integral