On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations
In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasov...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/109 |
| _version_ | 1797436794815381504 |
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| author | Cemil Tunç Osman Tunç Jen-Chih Yao |
| author_facet | Cemil Tunç Osman Tunç Jen-Chih Yao |
| author_sort | Cemil Tunç |
| collection | DOAJ |
| description | In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations. |
| first_indexed | 2024-03-09T11:07:46Z |
| format | Article |
| id | doaj.art-0e22c131521e4c329d23878db73a051b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:07:46Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-0e22c131521e4c329d23878db73a051b2023-12-01T00:51:58ZengMDPI AGSymmetry2073-89942022-12-0115110910.3390/sym15010109On the Enhanced New Qualitative Results of Nonlinear Integro-Differential EquationsCemil Tunç0Osman Tunç1Jen-Chih Yao2Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, TurkeyDepartment of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, TurkeyResearch Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, TaiwanIn this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations.https://www.mdpi.com/2073-8994/15/1/109nonlinearintegro-differential equationsstabilityconvergenceintegrabilityboundedness |
| spellingShingle | Cemil Tunç Osman Tunç Jen-Chih Yao On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations Symmetry nonlinear integro-differential equations stability convergence integrability boundedness |
| title | On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations |
| title_full | On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations |
| title_fullStr | On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations |
| title_full_unstemmed | On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations |
| title_short | On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations |
| title_sort | on the enhanced new qualitative results of nonlinear integro differential equations |
| topic | nonlinear integro-differential equations stability convergence integrability boundedness |
| url | https://www.mdpi.com/2073-8994/15/1/109 |
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