Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay
In this paper, we consider a system of random impulsive differential equations with infinite delay. When utilizing the nonlinear variation of Leray–Schauder’s fixed-point principles together with a technique based on separable vector-valued metrics to establish sufficient conditions for the existenc...
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MDPI AG
2023-12-01
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| Series: | Fractal and Fractional |
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| author | Abdelkader Moumen Fatima Zohra Ladrani Mohamed Ferhat Amin Benaissa Cherif Mohamed Bouye Keltoum Bouhali |
| author_facet | Abdelkader Moumen Fatima Zohra Ladrani Mohamed Ferhat Amin Benaissa Cherif Mohamed Bouye Keltoum Bouhali |
| author_sort | Abdelkader Moumen |
| collection | DOAJ |
| description | In this paper, we consider a system of random impulsive differential equations with infinite delay. When utilizing the nonlinear variation of Leray–Schauder’s fixed-point principles together with a technique based on separable vector-valued metrics to establish sufficient conditions for the existence of solutions, under suitable assumptions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mn>2</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϖ</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϖ</mi><mn>2</mn></msub></semantics></math></inline-formula>, which greatly enriched the existence literature on this system, there is, however, no hope to discuss the uniqueness result in a convex case. In the present study, we analyzed the influence of the impulsive and infinite delay on the solutions to our system. In addition, to the best of our acknowledge, there is no result concerning coupled random system in the presence of impulsive and infinite delay. |
| first_indexed | 2024-03-08T10:55:26Z |
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| language | English |
| last_indexed | 2024-03-08T10:55:26Z |
| publishDate | 2023-12-01 |
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| series | Fractal and Fractional |
| spelling | doaj.art-90c1664605cd44db8422f59dcee83f822024-01-26T16:35:09ZengMDPI AGFractal and Fractional2504-31102023-12-01811010.3390/fractalfract8010010Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite DelayAbdelkader Moumen0Fatima Zohra Ladrani1Mohamed Ferhat2Amin Benaissa Cherif3Mohamed Bouye4Keltoum Bouhali5Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaDepartment of Exact Sciences, Higher Training Teacher’s School of Oran Ammour Ahmed (ENSO), Oran 31000, AlgeriaDepartment of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir, Oran 31000, AlgeriaDepartment of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir, Oran 31000, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi ArabiaIn this paper, we consider a system of random impulsive differential equations with infinite delay. When utilizing the nonlinear variation of Leray–Schauder’s fixed-point principles together with a technique based on separable vector-valued metrics to establish sufficient conditions for the existence of solutions, under suitable assumptions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mn>2</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϖ</mi><mn>1</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϖ</mi><mn>2</mn></msub></semantics></math></inline-formula>, which greatly enriched the existence literature on this system, there is, however, no hope to discuss the uniqueness result in a convex case. In the present study, we analyzed the influence of the impulsive and infinite delay on the solutions to our system. In addition, to the best of our acknowledge, there is no result concerning coupled random system in the presence of impulsive and infinite delay.https://www.mdpi.com/2504-3110/8/1/10iterative methodsexistence of solutionsimpulsive equationsgeneralized banach spaceSchaefer’s fixed point theoremdifferential equations |
| spellingShingle | Abdelkader Moumen Fatima Zohra Ladrani Mohamed Ferhat Amin Benaissa Cherif Mohamed Bouye Keltoum Bouhali Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay Fractal and Fractional iterative methods existence of solutions impulsive equations generalized banach space Schaefer’s fixed point theorem differential equations |
| title | Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay |
| title_full | Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay |
| title_fullStr | Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay |
| title_full_unstemmed | Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay |
| title_short | Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay |
| title_sort | existence result for coupled random first order impulsive differential equations with infinite delay |
| topic | iterative methods existence of solutions impulsive equations generalized banach space Schaefer’s fixed point theorem differential equations |
| url | https://www.mdpi.com/2504-3110/8/1/10 |
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