Investigating the existence of solution for nonlinear Hadamard fractional functional integral equations via measure of noncompactness and its application

Pathak, Vijai Kumar; Mishra, Lakshmi Narayan

doi:10.1515/9783110785807-016

Cited by 1 publication

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“…The practical applications of nonlinear integral equations have recently received a lot of attention from studies that incorporate the same in distinct areas of knowledge that include mathematical modeling of real-world problems in various branches of science, like chemistry, physics, electrical networks, control of the dynamic system, optics, biological science, signal processing, and acoustic scattering [1][2][3][4][5][6][7]. Precisely, the recent development on these equations is focused on their solutions by using the measure of noncompactness technique [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator

Pathak

Mishra

2023

Math Methods in App Sciences

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In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previously in the literature. An example for a class of nonlinear functional integral equations is also presented to validate our main result. Finally, we propose the numerical method formed by the modified homotopy perturbation approach to resolving the problem with acceptable accuracy.

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