Existence and Uniqueness of Solutions for a Fractional Hybrid System with Nonseparated Integral Boundary Hybrid Conditions

Hannabou, Mohamed; Bouaouid, Mohamed; Hilal, Khalid

doi:10.1155/2022/3271626

Cited by 1 publication

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References 16 publications

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“…Integral equations are used in many disciplines of applied mathematics to explore and solve problems. See [1][2][3][4][5][6] for more information on the topic of two-dimensional nonlinear integral equations, which have long been of growing interest in many fields, including medicine [7], biology [8], physics [9], geography and fuzzy control [10]. According to the references [11][12][13][14][15][16], many problems in engineering [17], applied mathematics and mathematical physics [18] can be reduced to two-dimensional nonlinear integral equations with a symmetric and nonsymmetrical kernel.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Functions Approach via Nonlinear Integral Equations with Symmetric and Nonsymmetrical Kernel in Two Dimensions

et al. 2023

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The second kind of two-dimensional nonlinear integral equation (NIE) with symmetric and nonsymmetrical kernel is solved in the Banach space L2[0,1]×L2[0,1]. Here, the NIE’s existence and singular solution are described in this passage. Additionally, we use a numerical strategy that uses hybrid and block-pulse functions to obtain the approximate solution of the NIE in a two-dimensional problem. For this aim, the two-dimensional NIE will be reduced to a system of nonlinear algebraic equations (SNAEs). Then, the SNAEs can be solved numerically. This study focuses on showing the convergence analysis for the numerical approach and generating an estimate of the error. Examples are presented to prove the efficiency of the approach.

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