On ψ -Caputo Partial Hyperbolic Differential Equations with a Finite Delay

Abstract

In this work, we are concerned with some qualitative analyses of fractional-order partial hyperbolic functional differential equations under the $\psi$ -Caputo type. To be precise, we investigate the existence and uniqueness results based on the nonlinear alternative of the Leray-Schauder type and Banach contraction mapping. Moreover, we present two similar results to nonlocal problems. Then, the guarantee of the existence of solutions is shown by Ulam-Hyer’s stability. Two examples will be given to illustrate the abstract results. Eventually, some known results in the literature are extended.