A coupled non-separated system of Hadamard-type fractional differential equations

Abstract

In this article, we discuss the existence and uniqueness of solutions of a coupled non-separated system forfractional differential equations involving a Hadamard fractional derivative. The existence and uniquenessresults obtained in the present study are not only new but also cover some results corresponding to specialvalues of the parameters involved in the Caputo problems. These developed results are obtained by apply-ing Banach's fixed point theorem and Leray-Schauder's nonlinear alternative. An example is presented toillustrate our main results.