Existence, Uniqueness, and Stability Solutions of Nonlinear System of Integral Equations

Authors

  • Rizgar Issa Hasan Duhok Polytechnic University

DOI:

https://doi.org/10.15642/mantik.2020.6.2.76-82

Keywords:

Picard approximation method; Banach fixed point theorem; Integral equation

Abstract

The aim of this work is to study the existence, uniqueness, and stability solutions of a new nonlinear system of integral equation by using Picard approximation (successive approximation) method and Banach fixed point theorem. The study of such nonlinear integral equations is more general and leads us to improve to extend the result of Butris. Theorems on the existence and uniqueness of a solution are established under some necessary and sufficient conditions on closed and bounded domains (compact spaces).

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References

Butris, R. N., Solutions for the Volterra integral equations of the second kind, thesis, M.Sc., university of Mosul, Mosul, Iraq, (1984).

Butris, R. N., and Rafeq, A. Sh., Existence and uniqueness solution for nonlinear Volterra Integral Equation, J. Duhok Univ. Vol. 14, No. 1, (Pure and Eng. Sciences), (2011).

Butris, R. N. and Hussen Abdul-Qader, M. A. Some results in theory integro-differential equation of fractional order”, Iraq, Mosul, J. of Educ. And sci, Vol.49, (2001).

Goma, E. A. Sccessives approximation method of two points boundary problems, Ukrania,Math.,J.,Tom(33),Kiev,(1976).

Plaat, O., Ordinary Differential Equations, Holden-Day,Inc.San Rama, M.M., Ordinary Francisco,Cambridge,Londan,A msterdam ,(1971). .

Rama, M, M, Differential Equations Theory and Applications, United Kingdom, (1981).

Manouchehr Kazemi & Reza Ezzati, Existence of solutions for some nonlinear Volterra integral equations via Petryshyn’s fixed point theorem, Int. J. Nonlinear Anal. Appl. 9 No. 1, (2018).

Pakhshan Hasan & Nejmaddin Abdulla, Existence and uniqueness of solution for linear mixed Volterra-Fredholmintegral equations in Banach Space, American Journal of Computational and Applied Mathematics, 9(1), (2019).

Struble, R. A., “Nonlinear differential equations”, McGraw-Hill Book Company, Inc, New York, (1962).

Tricomi, F. G., Integral Equations, Turin University, Turin, Italy, (1965).

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Published

2020-10-31

How to Cite

Rizgar Issa Hasan. (2020). Existence, Uniqueness, and Stability Solutions of Nonlinear System of Integral Equations. Jurnal Matematika MANTIK, 6(2), 76–82. https://doi.org/10.15642/mantik.2020.6.2.76-82

Issue

Vol. 6 No. 2 (2020): Mathematics and Applied Mathematics

Section

Articles

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