The generalized Laplace transform method for a $\psi$-Caputo coupled system of Volterra integro-differential equations
Abstract
In this paper, we deal with the coupled system of
Volterra integro-differential equations of order $(p,q)$, The novelty of the considered problem is that it has been investigated under the $\psi$-Caputo fractional derivatives, which is more general than the works based on the well-known fractional derivatives such as (Caputo fractional derivative, Caputo–Hadamard fractional derivative and Caputo–Katugampola fractional derivative) for different values of the function $\psi$. We use the generalized Laplace transform method to find the solution then we obtain results on uniqueness using Banach's fixed point theorem. Next, we examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, a concrete application is given to illustrate the effectiveness of our main results.
Volterra integro-differential equations of order $(p,q)$, The novelty of the considered problem is that it has been investigated under the $\psi$-Caputo fractional derivatives, which is more general than the works based on the well-known fractional derivatives such as (Caputo fractional derivative, Caputo–Hadamard fractional derivative and Caputo–Katugampola fractional derivative) for different values of the function $\psi$. We use the generalized Laplace transform method to find the solution then we obtain results on uniqueness using Banach's fixed point theorem. Next, we examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, a concrete application is given to illustrate the effectiveness of our main results.
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