Topological degree theory and Caputo–Hadamard fractional boundary value problems

Abstract

Abstract We study two hybrid and non-hybrid fractional boundary value problems via the Caputo–Hadamard type derivatives. We seek the existence criteria for these two problems separately. By utilizing the generalized Dhage’s theorem, we derive desired results for an integral structure of solutions for the hybrid problems. Also by considering the special case as a non-hybrid boundary value problem (BVP), we establish other results based on the existing tools in the topological degree theory. In the end of the article, we examine our theoretical results by presenting some numerical examples to show the applicability of the analytical findings.

Keywords

• Caputo–Hadamard fractional BVP
• Condensing operator
• Degree theory
• The generalized Dhage’s theorem