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...
| Main Authors: | , , |
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| Format: | Article |
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Lviv Polytechnic National University
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102325/ |
| _version_ | 1848863773684662272 |
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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 |
| id | upm-102325 |
| 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/ |