Study on the integro-differential equations on $${C^1}({\mathbb {R}}_{+})$$

Tamimi, Hengameh; Saiedinezhad, Somayeh; Ghaemi, Mohammad Bagher

doi:10.1007/s40314-023-02239-4

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2024

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Cited by 2 publications

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“…The study of the existence of solutions for these equations heavily relies on condensing mappings, which are closely related to the M.N.C concept introduced by Kuratowski in 1930 [9]. Darbo's fixed point theorem, proposed by researchers, has gained significant attention in current research on integral models [6,16,17]. It generalizes both the classical Schauder fixed point and Banach contraction mapping principles, making it more popular among researchers [1,5,7,10].…”

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confidence: 99%

An Effective Approach Towards the Existence of a Nonlinear Functional Integro-differential Equations

Kazemi,

Deep,

Sahebi

2024

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The purpose of this paper is to demonstrate the existence of a solution for a functional integro-differential equation. To achieve this, we employ noncompactness measures and utilize fundamental fixed point theorems, such as Petryshyn’s fixed theorem, in the framwork of Banach spaces. Then this paper introduces a robust approach, based on fixed point theory, for proving the existence of solutions to the integro-differential equation. Finally, we present several examples of equations to demonstrate the applicability of our results to a broad range of integral equations.

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