Some results for a class of delayed fractional partial differential equations with Caputo–Hadamard derivative

Abstract

In this paper, we study the existence and uniqueness of the global solution to the Fractional Hyperbolic Systems of Partial Differential equations (FHyPDifS) by the Caputo–Hadamard fractional-order derivative. In addition, we give a new sufficient conditions for the finite time stability (FTS) of FHyPDifS for the Caputo–Hadamard fractional-order derivative. Finally, a numerical example is presented to illustrate our theoretical results.