Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps
This paper investigates a new class of fractional stochastic differential systems with non-Gaussian processes and Poisson jumps. Firstly, we examine the solvability results for the considered system. Furthermore, new stability results for the proposed system are derived. The findings are established...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/2/130 |
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| author | Nidhi Asthana Mohd Nadeem Rajesh Dhayal |
| author_facet | Nidhi Asthana Mohd Nadeem Rajesh Dhayal |
| author_sort | Nidhi Asthana |
| collection | DOAJ |
| description | This paper investigates a new class of fractional stochastic differential systems with non-Gaussian processes and Poisson jumps. Firstly, we examine the solvability results for the considered system. Furthermore, new stability results for the proposed system are derived. The findings are established through the application of Grönwall’s inequality, the successive approximation method, and the corollary of the Bihari inequality. Finally, the validity of the results is proved through an example. |
| format | Article |
| id | doaj-art-69235cdaee1b440697e445bbe79b6ad8 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-69235cdaee1b440697e445bbe79b6ad82025-08-20T03:12:11ZengMDPI AGFractal and Fractional2504-31102025-02-019213010.3390/fractalfract9020130Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson JumpsNidhi Asthana0Mohd Nadeem1Rajesh Dhayal2School of Technology Management & Engineering, SVKM’s Narsee Monjee Institute of Management Studies (NMIMS) Deemed-to-University, Indore 452005, IndiaDepartment of Mathematics, Kalindi College, University of Delhi, Delhi 110008, IndiaDepartment of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, IndiaThis paper investigates a new class of fractional stochastic differential systems with non-Gaussian processes and Poisson jumps. Firstly, we examine the solvability results for the considered system. Furthermore, new stability results for the proposed system are derived. The findings are established through the application of Grönwall’s inequality, the successive approximation method, and the corollary of the Bihari inequality. Finally, the validity of the results is proved through an example.https://www.mdpi.com/2504-3110/9/2/130fractional stochastic systemstabilitysuccessive approximation methodBihari inequality |
| spellingShingle | Nidhi Asthana Mohd Nadeem Rajesh Dhayal Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps Fractal and Fractional fractional stochastic system stability successive approximation method Bihari inequality |
| title | Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps |
| title_full | Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps |
| title_fullStr | Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps |
| title_full_unstemmed | Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps |
| title_short | Successive Approximation and Stability Analysis of Fractional Stochastic Differential Systems with Non-Gaussian Process and Poisson Jumps |
| title_sort | successive approximation and stability analysis of fractional stochastic differential systems with non gaussian process and poisson jumps |
| topic | fractional stochastic system stability successive approximation method Bihari inequality |
| url | https://www.mdpi.com/2504-3110/9/2/130 |
| work_keys_str_mv | AT nidhiasthana successiveapproximationandstabilityanalysisoffractionalstochasticdifferentialsystemswithnongaussianprocessandpoissonjumps AT mohdnadeem successiveapproximationandstabilityanalysisoffractionalstochasticdifferentialsystemswithnongaussianprocessandpoissonjumps AT rajeshdhayal successiveapproximationandstabilityanalysisoffractionalstochasticdifferentialsystemswithnongaussianprocessandpoissonjumps |