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Prospects for Applied Mathematics and Data Analysis

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Prospects for Applied Mathematics and Data Analysis
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Volume 4 • Issue 2 • PP: 23-36 • 2024

Stability Solution of Fractional Randomly System

Eman Ahmad Hussen 1*
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Sameh ALargeh 2
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1PhD Student, Homs University, College of Science, Homs, Syria
2Faculty Member, Homs University, Faculty of Science, Homs, Syria
* Corresponding Author.
DOI https://doi.org/10.54216/PAMDA.040203
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: September 14, 2024 Revised: November 18, 2024 Accepted: December 31, 2024
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Abstract

In this paper, we study stability Solution of Fractional Randomly System. Two methods are provided to check the stability of such system in mean sense. The first method is based on integral inequalities. The second method is based on Lyapunov function. Stable in mean sense, asymptotically stable in mean sense are shown by using generalized Gromwell inequality. Stable in mean sense, asymptotically stable in mean sense, Mittag-Leffler stable in mean sense are shown by using generalized Lyapunov method.

Keywords

Randomly Parameters Norm expected value Lyapunov function Integral inequalities Stable Mean sense Laplace transform Fractional derivative

References

[1]       J. Sabatier, O. P. Agrawal, and J. A. Machado, "Advance in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering," Dordrecht, The Netherlands: Springer, 2007.

[2]       B. Ahmad, M. M. Matar, and O. M. El-Salmy, "Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations," International Journal of Analysis and Applications, vol. 15, no. 1, pp. 86-101, 2017.

[3]       D. Matignon, "Stability results for Fractional Differential Equations with Applications to Control Processing," in Proceedings of the IMACS-SMC, vol. 2, pp. 963-968, 1996.

[4]       W. Deng, C. Li, and Q. Guo, "Analysis of Fractional Differential Equations with Multi-Orders," Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society, vol. 15, no. 2, pp. 173-182, 2007.

[5]       N. Agulla-Camacho, M. A. Duarte-Mermoud, and J. A. Gallegos, "Lyapunov Functions for Fractional Order Systems," Communications in Nonlinear Science and Numerical Simulation, vol. 19, pp. 2951-2957, 2014.

[6]       T. Burton and B. Zhang, "Fixed Points and Fractional Differential Equations," Fixed Points Theory, vol. 13, pp. 313-325, 2013.

[7]       M. Ilolov, K. S. Kuchakshoev, and J. Sh. Rahmatov, "Fractional Stochastic Evolutions: White Noise Models," Communications on Stochastic Analysis, vol. 14, no. 3, pp. 55-69, 2020.

[8]       A. Yu and V. Veretennikov, "On Weak Solutions of Highly Degenerate SDEs," Automation and Remote Control, vol. 83, no. 3, pp. 398-410, 2020.

[9]       D. Wang, X. L. Ding, and J. Nieto, "Stability Analysis of Fractional Order Systems with Randomly Time Varying Parameters," Nonlinear Analysis: Modeling and Control, vol. 26, no. 3, pp. 440-460, 2021.

[10]    A. Ahmadova and N. I. Mahmudov, "Asymptotic Stability Analysis of Riemann-Liouville Fractional Stochastic Neutral Differential Equations," Miskolc Mathematical Notes, vol. 22, no. 2, pp. 503-520, 2021.

[11]    M. Popolizio, "On the Matrix Mittag-Leffler Function: Theoretical Properties and Numerical Computation," 2019.

[12]    I. Podlubny, "Fractional Differential Equations," San Diego, CA, USA: Academic Press, 1999.

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Hussen, Eman Ahmad, ALargeh, Sameh. "Stability Solution of Fractional Randomly System." Prospects for Applied Mathematics and Data Analysis, vol. Volume 4, no. Issue 2, 2024, pp. 23-36. DOI: https://doi.org/10.54216/PAMDA.040203
Hussen, E., ALargeh, S. (2024). Stability Solution of Fractional Randomly System. Prospects for Applied Mathematics and Data Analysis, Volume 4(Issue 2), 23-36. DOI: https://doi.org/10.54216/PAMDA.040203
Hussen, Eman Ahmad, ALargeh, Sameh. "Stability Solution of Fractional Randomly System." Prospects for Applied Mathematics and Data Analysis Volume 4, no. Issue 2 (2024): 23-36. DOI: https://doi.org/10.54216/PAMDA.040203
Hussen, E., ALargeh, S. (2024) 'Stability Solution of Fractional Randomly System', Prospects for Applied Mathematics and Data Analysis, Volume 4(Issue 2), pp. 23-36. DOI: https://doi.org/10.54216/PAMDA.040203
Hussen E, ALargeh S. Stability Solution of Fractional Randomly System. Prospects for Applied Mathematics and Data Analysis. 2024;Volume 4(Issue 2):23-36. DOI: https://doi.org/10.54216/PAMDA.040203
E. Hussen, S. ALargeh, "Stability Solution of Fractional Randomly System," Prospects for Applied Mathematics and Data Analysis, vol. Volume 4, no. Issue 2, pp. 23-36, 2024. DOI: https://doi.org/10.54216/PAMDA.040203
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