On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method

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DOI: https://doi.org/10.28924/2291-8639-20-2022-35
Published: Jul 20, 2022
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A. S. Rahby, M. A. Abdou, G. A. Mosa, On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method, Int. J. Anal. Appl., 20 (2022), 35.

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A. S. Rahby, M. A. Abdou, G. A. Mosa

Abstract

In this paper, we discuss the existence and uniqueness of the solution of the second kind nonlinear Volterra-Fredholm integral equations (NV-FIEs) which appear in mathematical modeling of many phenomena, using Picard’s method. In addition, we use Banach fixed point theorem to show the solvability of the first kind NV-FIEs. Moreover, we utilize the homotopy analysis method (HAM) to approximate the solution and the convergence of the method is investigated. Finally, some examples are presented and the numerical results are discussed to show the validity of the theoretical results.

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