Nonlocal fuzzy fractional stochastic evolution equations with fractional Brownian motion of order (1,2)

Kinda Abuasbeh; Ramsha Shafqat; Azmat Ullah Khan Niazi; Muath Awadalla; Kinda Abuasbeh; Ramsha Shafqat; Azmat Ullah Khan Niazi; Muath Awadalla

doi:10.3934/math.20221062

AIMS Mathematics

2022, Volume 7, Issue 10: 19344-19358. doi: 10.3934/math.20221062

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Research article

Nonlocal fuzzy fractional stochastic evolution equations with fractional Brownian motion of order (1,2)

1.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia
2.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan

Received: 06 July 2022 Revised: 21 August 2022 Accepted: 28 August 2022 Published: 01 September 2022
MSC : 34A07, 34A08, 60G22

In this manuscript, we formulate the system of fuzzy stochastic fractional evolution equations (FSFEEs) driven by fractional Brownian motion. We find the results about the existence-uniqueness of the formulated system by using the Lipschitizian conditions. By using these conditions we have also investigated the exponential stability of the solution for the above system driven by fractional Brownian motion. Finally, the applications in financial mathematics are presented and the use of financial mathematics in the fractional Black and Scholes model is also discussed. An example is propounded to show the applicability of our results.
- fuzzy set theory,
- fuzzy stochastic processes,
- fuzzy stochastic differential equation,
- fractional Brownian motion
Citation: Kinda Abuasbeh, Ramsha Shafqat, Azmat Ullah Khan Niazi, Muath Awadalla. Nonlocal fuzzy fractional stochastic evolution equations with fractional Brownian motion of order (1,2)[J]. AIMS Mathematics, 2022, 7(10): 19344-19358. doi: 10.3934/math.20221062

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Abstract

In this manuscript, we formulate the system of fuzzy stochastic fractional evolution equations (FSFEEs) driven by fractional Brownian motion. We find the results about the existence-uniqueness of the formulated system by using the Lipschitizian conditions. By using these conditions we have also investigated the exponential stability of the solution for the above system driven by fractional Brownian motion. Finally, the applications in financial mathematics are presented and the use of financial mathematics in the fractional Black and Scholes model is also discussed. An example is propounded to show the applicability of our results.

References

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