2022
DOI: 10.52737/18291163-2020.12.7-1-8
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Existence of a solution in the Holder space for a nonlinear functional integral equation

Abstract: This article is entirely devoted to the application of the measure of noncompactness defined in the Holder space. Here the emphasis is on the study of the nonlinear functional integral equation with changed arguments. Precisely, the existence of a solution is obtained by employing the Darbo fixed point theorem under certain hypotheses. Finally, we provide a tangible example which supports our results.

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Cited by 7 publications
(2 citation statements)
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“…In either case, if one concentrate upon integer order operations only, then that leads to classical pantograph integro-differential [23,29] and integro-difference [6,37] equations, respectively. For the above cases the theoretical investigation related to existence and uniqueness of solution have been carried out by J. M. Cushing [14], A. Aghajani et al [2], K. Balachandran et al [7], Sarkar et al [31], Saha et al [30], Gupta et al [19], S. Etemad et al [8], B. Ahmad et al [3] and many other researchers. However, all the previously published works are primarily focused on separate cases only.…”
Section: Introductionmentioning
confidence: 99%
“…In either case, if one concentrate upon integer order operations only, then that leads to classical pantograph integro-differential [23,29] and integro-difference [6,37] equations, respectively. For the above cases the theoretical investigation related to existence and uniqueness of solution have been carried out by J. M. Cushing [14], A. Aghajani et al [2], K. Balachandran et al [7], Sarkar et al [31], Saha et al [30], Gupta et al [19], S. Etemad et al [8], B. Ahmad et al [3] and many other researchers. However, all the previously published works are primarily focused on separate cases only.…”
Section: Introductionmentioning
confidence: 99%
“…Nowadays, many authors have proposed and developed numerical and analytical techniques for fractional order differential equations, which are: the variational iteration transform method (VITM) [6], Laplace decomposition method (LDM) [7], homotopy perturbation transform method (HPTM) [8], conformable fractional differential transform method (CFDTM) [9], natural reduced differential transform method (NRDTM) [10], boundary element method (BEM) [11], finite difference method (FDM) [12], and so on.…”
Section: Introductionmentioning
confidence: 99%