Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay
In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/239 |
| _version_ | 1797504522639114240 |
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| author | Mahmoud Abouagwa Rashad A. R. Bantan Waleed Almutiry Anas D. Khalaf Mohammed Elgarhy |
| author_facet | Mahmoud Abouagwa Rashad A. R. Bantan Waleed Almutiry Anas D. Khalaf Mohammed Elgarhy |
| author_sort | Mahmoud Abouagwa |
| collection | DOAJ |
| description | In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results. |
| first_indexed | 2024-03-10T04:05:47Z |
| format | Article |
| id | doaj.art-e9e74f824a9a4c68a2533d89c4e84313 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:47Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e9e74f824a9a4c68a2533d89c4e843132023-11-23T08:24:11ZengMDPI AGFractal and Fractional2504-31102021-11-015423910.3390/fractalfract5040239Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable DelayMahmoud Abouagwa0Rashad A. R. Bantan1Waleed Almutiry2Anas D. Khalaf3Mohammed Elgarhy4Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptDepartment of Marine Geology, Faulty of Marine Science, King AbdulAziz University, Jeddah 21551, Saudi ArabiaDepartment of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi ArabiaMinsitry of Education, General Directorate of Education in Saladin, Tikrit 34001, IraqThe Higher Institute of Commercial Sciences, Al Mahalla Alkubra, Algarbia 31951, EgyptIn this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.https://www.mdpi.com/2504-3110/5/4/239fractional differential system of neutral typefractional brownian motionfractional calculusPoisson jumpCarathéodory approximation |
| spellingShingle | Mahmoud Abouagwa Rashad A. R. Bantan Waleed Almutiry Anas D. Khalaf Mohammed Elgarhy Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay Fractal and Fractional fractional differential system of neutral type fractional brownian motion fractional calculus Poisson jump Carathéodory approximation |
| title | Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay |
| title_full | Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay |
| title_fullStr | Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay |
| title_full_unstemmed | Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay |
| title_short | Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay |
| title_sort | mixed caputo fractional neutral stochastic differential equations with impulses and variable delay |
| topic | fractional differential system of neutral type fractional brownian motion fractional calculus Poisson jump Carathéodory approximation |
| url | https://www.mdpi.com/2504-3110/5/4/239 |
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