Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima

In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel combined with the method of regularization, we obtain an implici...

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Main Authors: Yuldashev, T. K., Eshkuvatov, Z. K., Nik Long, N. M. A.
Format: Article
Published: Lviv Polytechnic National University 2022
Online Access:http://psasir.upm.edu.my/id/eprint/102325/
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author Yuldashev, T. K.
Eshkuvatov, Z. K.
Nik Long, N. M. A.
author_facet Yuldashev, T. K.
Eshkuvatov, Z. K.
Nik Long, N. M. A.
author_sort Yuldashev, T. K.
building UPM Institutional Repository
collection Online Access
description In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel combined with the method of regularization, we obtain an implicit the first-order functional-differential equation with the nonlinear maxima. Initial boundary conditions are used to ensure the solution uniqueness. In order to use the method of a successive approximations and prove the one value solvability, the obtained implicit functional-differential equation is transformed to the nonlinear Volterra type integro-differential equation with the nonlinear maxima.
first_indexed 2025-11-15T13:38:15Z
format Article
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institution Universiti Putra Malaysia
institution_category Local University
last_indexed 2025-11-15T13:38:15Z
publishDate 2022
publisher Lviv Polytechnic National University
recordtype eprints
repository_type Digital Repository
spelling upm-1023252023-07-10T00:15:07Z http://psasir.upm.edu.my/id/eprint/102325/ Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima Yuldashev, T. K. Eshkuvatov, Z. K. Nik Long, N. M. A. In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel combined with the method of regularization, we obtain an implicit the first-order functional-differential equation with the nonlinear maxima. Initial boundary conditions are used to ensure the solution uniqueness. In order to use the method of a successive approximations and prove the one value solvability, the obtained implicit functional-differential equation is transformed to the nonlinear Volterra type integro-differential equation with the nonlinear maxima. Lviv Polytechnic National University 2022 Article PeerReviewed Yuldashev, T. K. and Eshkuvatov, Z. K. and Nik Long, N. M. A. (2022) Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima. Mathematical Modeling and Computing, 9 (1). 74 - 82. ISSN 2312-9794 https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-9-number-1-2022/nonlinear-first-kind-fredholm-integro-differential 10.23939/mmc2022.01.074
spellingShingle Yuldashev, T. K.
Eshkuvatov, Z. K.
Nik Long, N. M. A.
Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
title Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
title_full Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
title_fullStr Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
title_full_unstemmed Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
title_short Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
title_sort nonlinear the first kind fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima
url http://psasir.upm.edu.my/id/eprint/102325/
http://psasir.upm.edu.my/id/eprint/102325/
http://psasir.upm.edu.my/id/eprint/102325/