Existence of fuzzy fractional stochastic differential system with impulses

Priyadharsini, J.; Balasubramaniam, P.

doi:10.1007/s40314-020-01229-0

Cited by 13 publications

(5 citation statements)

References 25 publications

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“…After finishing the work of this paper, we will be devoted to studying the averaging principle of fuzzy fractional stochastic differential equations. According to the relevant literatures, 37,38 one of the most important works is how to embed one space into another. In addition, how to deal with random terms in fuzzy sense is a difficult but interesting subject, which will be discussed carefully in our following work.…”

Section: Discussionmentioning

confidence: 99%

The existence and averaging principle for stochastic fractional differential equations with impulses

Zou

Luo

2022

Math Methods in App Sciences

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In this paper, a class of fractional stochastic differential equations (SFDEs) with impulses is considered. By virtue of Mönch's fixed point theorem and Banach contraction principle, we explore the existence and uniqueness of solutions to the addressed system. Furthermore, with the aid of the Jensen inequality, Hölder inequality, Burkholder-Davis-Gundy inequality, Grönwall-Bellman inequality, and some novel assumptions, the averaging principle of our considered system is obtained. At the end of this paper, an example is provided to illustrate the theoretical results.

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Section: Discussionmentioning

confidence: 99%

The existence and averaging principle for stochastic fractional differential equations with impulses

Zou

Luo

2022

Math Methods in App Sciences

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“…Granular fuzzy PID control as a combination of the concept of PID controller and granular derivative and granular integral has been proposed in [21] . In [22] , the existence and uniqueness results have been obtained for impulsive fuzzy FSDS with granular derivative and using contraction principle. In [23] , a class of granular type optimality guidelines for the fuzzy multi-objective optimizations based on vector granular convexity and granular differentiability has been introduced.…”

Section: Some Of the Applications Of Granular Derivativementioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

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“…For more work on the study of random impulsive differential equations, we refer the reader to [12][13][14][15][16][17][18] and the references therein. In particular, Anguraj et al [16] considered the existence and stability results for a class of random impulsive fractional pantograph equations, and Priyadharsini and Balasubramaniam [19] studied existence and uniqueness results for fuzzy fractional stochastic pantograph differential equations. Recently, Shu et al [18] made the first step in that they investigated the existence and Hyers-Ulam stability of a class of random impulsive stochastic functional differential equations with infinite delays under Lipschitz conditions on a bounded and closed interval.…”

Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Gao,

2024

Mathematics

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In this paper, we study the existence, uniqueness and Hyers–Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer’s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers–Ulam stable via Gronwall’s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

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Existence of fuzzy fractional stochastic differential system with impulses

Cited by 13 publications

References 25 publications

The existence and averaging principle for stochastic fractional differential equations with impulses

The existence and averaging principle for stochastic fractional differential equations with impulses

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

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