On the nonlinear Hadamard-type integro-differential equation

Abstract

This paper studies uniqueness of solutions for a nonlinear Hadamard-type integro-differential equation in the Banach space of absolutely continuous functions based on Babenko’s approach and Banach’s contraction principle. We also include two illustrative examples to demonstrate the use of 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.…”