Existence theory for a fractional order system governed by the Hadamard-Caputo derivative

In recent, the primary aim of the research is focussed on investigating new generalizations of the classical fractional derivatives. The Caputo-Hadamard derivative is a modification of the Hadamard fractional derivative in a Caputo sense. In this paper, we propose a non-local fractional order system involving the Hadamard-Caputo fractional derivative and examine the existence and uniqueness (EU) of a solution to the considered generalized system incorporating boundary value conditions. The Krasnoselskii fixed point theorem and the Banach contraction mapping principle, the well-known fixed point theories, corroborate our findings. The results can be improved from both theoretical and applied perspectives owing to the generalized derivatives. In order to confirm the applicability of obtained result an example is presented.