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

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

MMC.
2022;
Volume 9, Number 1
: pp. 74–82
https://doi.org/10.23939/mmc2022.01.074
Received: July 07, 2021
Accepted: November 17, 2021

Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 74–82 (2022)

Authors:
  1. T. K. Yuldashev
  2. Z. K. Eshkuvatov
  3. N. M. A. Nik Long
1
Uzbek-Israel Joint Faculty of High Technology and Engineering Mathematics, National University of Uzbekistan
2
Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu; Independent reseacher, Faculty of Applied Mathematics and Intellectual Technologies, National University of Uzbekistan
3
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia

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.

integro-differential equation
nonlinear functional-differential equation
degenerate kernel
nonlinear maxima
regularization
one value solvability
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