Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays

Xue, Wang; Luo, Danfeng; Zhu, Quanxin

doi:10.1016/j.chaos.2022.111822

Cited by 63 publications

(18 citation statements)

References 27 publications

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“…Fractional calculus has been of great interest in the past few decades since it has been confirmed to be a powerful tool with more accurate results in the mathematical modeling of many phenomena occurring in physics and engineering. This is due to its wide application in various areas, particularly in control engineering [1,2], physics [3,4], economics [5], and image processing [6]; for more detail, we can pay attention to the monographs [7][8][9] and previous studies [10][11][12][13][14].…”

Section: Previous Workmentioning

confidence: 99%

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Huang

Luo

2023

Math Methods in App Sciences

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In this article, we consider the relatively exact controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. First, we derive the solution of linear FSDS via delayed matrix functions of Mittag-Leffler (M-L). Subsequently, by virtue of the controllability Grammian matrix, we explore the relatively exact controllability of linear FSDS. In addition, with the aid of Jensen's inequality, Hölder's inequality, and Itô's isometry, the existence and uniqueness of the considered nonlinear FSDS are investigated by employing Banach contraction principle. Thereafter, the relatively exact controllability of nonlinear FSDS is discussed. Finally, the theoretical results are supported through examples.

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Section: Previous Workmentioning

confidence: 99%

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Huang

Luo

2023

Math Methods in App Sciences

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“…Some researchers went deeper into their research and verified the stability of the solutions to these equations (see [26,27]). Furthermore, many specialists in the field have paid attention to hybrid fractional differential equations; the importance of fractional hybrid differential equations is that they have a different dynamic than ordinary differential equations and that the hybrid type describes the nonlinear relationship in the derivative of the hybrid function (see [28][29][30][31]).…”

Section: X(t) G(t X(t))mentioning

confidence: 99%

On System of Nonlinear Sequential Hybrid Fractional Differential Equations

Awadalla

Abuasbeh

2022

Mathematical Problems in Engineering

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In this study, the existence and uniqueness of the solution for a system consisting of sequential fractional differential equations that contain Caputo–Hadamard (CH) derivative are verified. To study the existence and uniqueness of these solutions, some of the most important results from the fixed point theorems in Banach space were used. A practical example is also given to support the theoretical side that was obtained.

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“…It was found that various, especially interdisciplinary, applications can be elegantly modeled with the help of fractional derivatives [1][2][3][4]. See also the recent works of [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

et al. 2023

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We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter H^∈(1/2,1). Using fixed point techniques, a q-resolvent family, and fractional calculus, we discuss the existence of a piecewise continuous mild solution for the proposed system. Moreover, under appropriate conditions, we investigate the approximate controllability of the considered system. Finally, the main results are demonstrated with an illustrative example.

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Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays

Cited by 63 publications

References 27 publications

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

On System of Nonlinear Sequential Hybrid Fractional Differential Equations

Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

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