A Numerical Approach of Handling Fractional Stochastic Differential Equations
This work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, a novel three-point fractional formula for approximating the Riemann–Liouville integrator is established, and then it is applied to generate approximate solutions for fractional...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/4/388 |
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| author | Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh |
| author_facet | Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh |
| author_sort | Iqbal M. Batiha |
| collection | DOAJ |
| description | This work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, a novel three-point fractional formula for approximating the Riemann–Liouville integrator is established, and then it is applied to generate approximate solutions for fractional stochastic differential equations. Such a formula is derived with the use of the generalized Taylor theorem coupled with a recent definition of the definite fractional integral. Our approach is compared with the approximate solution generated by the Euler–Maruyama method and the exact solution for the purpose of verifying our findings. |
| first_indexed | 2024-03-11T05:15:19Z |
| format | Article |
| id | doaj.art-b50db88a8a334c958bc289c775b19eae |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T05:15:19Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b50db88a8a334c958bc289c775b19eae2023-11-17T18:19:40ZengMDPI AGAxioms2075-16802023-04-0112438810.3390/axioms12040388A Numerical Approach of Handling Fractional Stochastic Differential EquationsIqbal M. Batiha0Ahmad A. Abubaker1Iqbal H. Jebril2Suha B. Al-Shaikh3Khaled Matarneh4Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, JordanFaculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaDepartment of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, JordanFaculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaFaculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaThis work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, a novel three-point fractional formula for approximating the Riemann–Liouville integrator is established, and then it is applied to generate approximate solutions for fractional stochastic differential equations. Such a formula is derived with the use of the generalized Taylor theorem coupled with a recent definition of the definite fractional integral. Our approach is compared with the approximate solution generated by the Euler–Maruyama method and the exact solution for the purpose of verifying our findings.https://www.mdpi.com/2075-1680/12/4/388fractional calculusfractional stochastic differential equationsEuler–Maruyama method |
| spellingShingle | Iqbal M. Batiha Ahmad A. Abubaker Iqbal H. Jebril Suha B. Al-Shaikh Khaled Matarneh A Numerical Approach of Handling Fractional Stochastic Differential Equations Axioms fractional calculus fractional stochastic differential equations Euler–Maruyama method |
| title | A Numerical Approach of Handling Fractional Stochastic Differential Equations |
| title_full | A Numerical Approach of Handling Fractional Stochastic Differential Equations |
| title_fullStr | A Numerical Approach of Handling Fractional Stochastic Differential Equations |
| title_full_unstemmed | A Numerical Approach of Handling Fractional Stochastic Differential Equations |
| title_short | A Numerical Approach of Handling Fractional Stochastic Differential Equations |
| title_sort | numerical approach of handling fractional stochastic differential equations |
| topic | fractional calculus fractional stochastic differential equations Euler–Maruyama method |
| url | https://www.mdpi.com/2075-1680/12/4/388 |
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