A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay
This paper presents an analysis of the existence, uniqueness, and stability of solutions to fractional neutral Volterra-Fredholm integro-differential equations, incorporating Caputo fractional derivatives and semigroup operators with state-dependent delays. By employing Krasnoselskii’s fixed point t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/20 |
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| author | Prabakaran Raghavendran Tharmalingam Gunasekar Junaid Ahmad Walid Emam |
| author_facet | Prabakaran Raghavendran Tharmalingam Gunasekar Junaid Ahmad Walid Emam |
| author_sort | Prabakaran Raghavendran |
| collection | DOAJ |
| description | This paper presents an analysis of the existence, uniqueness, and stability of solutions to fractional neutral Volterra-Fredholm integro-differential equations, incorporating Caputo fractional derivatives and semigroup operators with state-dependent delays. By employing Krasnoselskii’s fixed point theorem, conditions under which solutions exist are established. To ensure uniqueness, the Banach Contraction Principle is applied, and the contraction condition is verified. Stability is analyzed using Ulam’s stability concept, emphasizing the resilience of solutions to perturbations and providing insights into their long-term behavior. An example is included, accompanied by graphical analysis that visualizes the solutions and their dynamic properties. |
| format | Article |
| id | doaj-art-958d09e0d4984d0c93c6542086c8fc37 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-958d09e0d4984d0c93c6542086c8fc372025-01-24T13:33:23ZengMDPI AGFractal and Fractional2504-31102024-12-01912010.3390/fractalfract9010020A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent DelayPrabakaran Raghavendran0Tharmalingam Gunasekar1Junaid Ahmad2Walid Emam3Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, IndiaDepartment of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, IndiaDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThis paper presents an analysis of the existence, uniqueness, and stability of solutions to fractional neutral Volterra-Fredholm integro-differential equations, incorporating Caputo fractional derivatives and semigroup operators with state-dependent delays. By employing Krasnoselskii’s fixed point theorem, conditions under which solutions exist are established. To ensure uniqueness, the Banach Contraction Principle is applied, and the contraction condition is verified. Stability is analyzed using Ulam’s stability concept, emphasizing the resilience of solutions to perturbations and providing insights into their long-term behavior. An example is included, accompanied by graphical analysis that visualizes the solutions and their dynamic properties.https://www.mdpi.com/2504-3110/9/1/20Caputo fractional derivativeBanach contraction principleKrasnoselskii’s fixed point theoremUlam stabilitysemigroup theory |
| spellingShingle | Prabakaran Raghavendran Tharmalingam Gunasekar Junaid Ahmad Walid Emam A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay Fractal and Fractional Caputo fractional derivative Banach contraction principle Krasnoselskii’s fixed point theorem Ulam stability semigroup theory |
| title | A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay |
| title_full | A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay |
| title_fullStr | A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay |
| title_full_unstemmed | A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay |
| title_short | A Study on the Existence, Uniqueness, and Stability of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay |
| title_sort | study on the existence uniqueness and stability of fractional neutral volterra fredholm integro differential equations with state dependent delay |
| topic | Caputo fractional derivative Banach contraction principle Krasnoselskii’s fixed point theorem Ulam stability semigroup theory |
| url | https://www.mdpi.com/2504-3110/9/1/20 |
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