Uniqueness of the Hadamard-type integral equations

Abstract

The goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko’s approach and Banach’s contraction principle. We also present several examples for illustration of the main theorems.

Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations

“…Also, some pertinent examples have been provided to justify the main results. The obtained results in this study extended and developed the current results introduced by [17,18]. We have already concluded that our results are valid when the left-hand side of the considered problem (1) involves many FDs and IDs as shown in Remark 22.…”

“…Specifically, ψ-Caputo type FDEs with initial, boundary, and nonlocal conditions have been investigated by many researchers using fixed-point theories, see Almeida et al [11,12], Abdo et al [13], and Wahash et al [14]. A recent survey on ψ-Caputo type FDEs can be found in [15][16][17][18]. For more results in this direction, we refer to interesting works provided by Zhang et al [19], Zhao et al [20], Baitiche et al [21], Benchohra et al [22], Ravichandran et al [23], Trujillo et al [24], and Furati et al [25].…”

“…Li in [17,18] investigated some interesting results of the integral equations and the integro-differential equations involving Hadamard-type. In this work, our goal is to intend to address a general extension of these studies.…”

Analytical Investigation of the Existence of Solutions for a System of Nonlinear Hadamard-Type Integro-Differential Equations Based upon the Multivariate Mittag-Leffler Function

“…We assume that the functions f 1 (x, z 1 , z 2 ) and f 2 (x, z 1 , z 2 ) satisfy the Lipschitz conditions in the second and third variables. Then, the uniqueness of a system for the nonlinear Hadamard-type integro-differential equations, with all µ ∈ R and positive orders, in the Banach space X µ (a, b) × X µ (a, b), was studied very recently by Li in [29] by using Banach's fixed point theorem.…”