Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control
In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochas...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/5394528 |
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| _version_ | 1832552801276788736 |
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| author | Fathalla A. Rihan Chinnathambi Rajivganthi Palanisamy Muthukumar |
| author_facet | Fathalla A. Rihan Chinnathambi Rajivganthi Palanisamy Muthukumar |
| author_sort | Fathalla A. Rihan |
| collection | DOAJ |
| description | In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results. |
| format | Article |
| id | doaj-art-affa932871ad485cb72e820ce748a851 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-affa932871ad485cb72e820ce748a8512025-02-03T05:57:46ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/53945285394528Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal ControlFathalla A. Rihan0Chinnathambi Rajivganthi1Palanisamy Muthukumar2Department of Mathematical Sciences, College of Science, UAE University, Al-Ain 15551, UAEDepartment of Mathematical Sciences, College of Science, UAE University, Al-Ain 15551, UAEDepartment of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu 624 302, IndiaIn this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.http://dx.doi.org/10.1155/2017/5394528 |
| spellingShingle | Fathalla A. Rihan Chinnathambi Rajivganthi Palanisamy Muthukumar Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control Discrete Dynamics in Nature and Society |
| title | Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control |
| title_full | Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control |
| title_fullStr | Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control |
| title_full_unstemmed | Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control |
| title_short | Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control |
| title_sort | fractional stochastic differential equations with hilfer fractional derivative poisson jumps and optimal control |
| url | http://dx.doi.org/10.1155/2017/5394528 |
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