Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model

Kaviya, R.; Priyanka, M.; Muthukumar, P.

doi:10.1016/j.chaos.2022.112070

Cited by 10 publications

(1 citation statement)

References 31 publications

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“…Fractional calculus and fractional differential equations (FDEs) have been widely applied in mechanics, physics, biological and the other fields of science and engineering [1][2][3][4][5][6]. In recent decades, there has been an explosion in searching for the existence, uniqueness, stability and controllability of impulsive differential equations (IDEs) as researchers in epidemic, optimal control, mechanical and engineering studies are pouring into the field of research; we refer the reader to [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Existence and Ulam Type Stability for Impulsive Fractional Differential Systems with Pure Delay

Chen

2022

Fractal Fract

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Through literature retrieval and classification, it can be found that for the fractional delay impulse differential system, the existence and uniqueness of the solution and UHR stability of the fractional delay impulse differential system are rarely studied by using the polynomial function of the fractional delay impulse matrix. In this paper, we firstly introduce a new concept of impulsive delayed Mittag–Leffler type solution vector function, which helps us to construct a representation of an exact solution for the linear impulsive fractional differential delay equations (IFDDEs). Secondly, by using Banach’s and Schauder’s fixed point theorems, we derive some sufficient conditions to guarantee the existence and uniqueness of solutions of nonlinear IFDDEs. Finally, we obtain the Ulam–Hyers stability (UHs) and Ulam–Hyers–Rassias stability (UHRs) for a class of nonlinear IFDDEs.

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