Hadamard Fractional Differential Equations on an Unbounded Domain with Integro-initial Conditions

Abstract

In this paper, we introduce and investigate a Hadamard-type fractional differential equation on the interval \((1, \infty )\) equipped with a new class of logarithmic type integro-initial conditions. We apply the Leggett–Williams fixed point theorem and the concept of iterative positive solutions to establish the existence of solutions for the problem at hand. Our results are new and enrich the literature on Hadamard-type fractional differential equations on the infinite domain. Examples illustrating the main results are presented.