Multi-stability of non homogenous vector-valued fractional differential equations in matrix-valued Menger spaces

Aderyani, Safoura Rezaei; Saadati, Reza; Abdeljawad, Thabet; Mlaiki, Nabil

doi:10.1016/j.aej.2022.03.053

Cited by 19 publications

(6 citation statements)

References 20 publications

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“…The MVRN space (J, Ψ, ) is defined and studied in [21,29]. A triple (J, Ψ, ) is said to be an MVRN space if for each χ, χ ′ ∈ J, and ψ > 0, we have (1)…”

Section: Random Normed (Mvrn) Spacesmentioning

confidence: 99%

“…Here, we consider the Mittag-Leffler matrices [21] with parameters P 1 , P 2 > 0, and [H] n×n which are defined by 38]). The fractional-order delayed matrix cosine, and the fractional-order delayed matrix sine of a polynomial of degree 2jP on χ ∈ [(j − 1)Y, jY ) identified at the nodes χ = jY, j = 0, 1, • • • , are, respectively, given by cos Y,P…”

Section: Fractional-order Delayed Matrix Sine and Cosinementioning

confidence: 99%

“…The stability of differential linear equations of the first order was studied in [16,17], Riccati equations were studied in [18], Bernoulli equations in [19], and Ulam stability of partial differential equations was investigated by Rassias and Prastaro in [20][21][22]; the authors presented a different concept of perturbation stability in the Ulam sense.…”

mentioning

confidence: 99%

“…As will be shown, by introducing the concept of time-stamped fuzzy sets and distribution functions that have a dynamic state, we can choose the best approximation of the solution of a fractional-order system at any time. Motivated by [21,22], we study the following fractional-order system:…”

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confidence: 99%

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Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Aderyani,

Saadati,

O’Regan

et al. 2024

Mathematics

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We apply known special functions from the literature (and these include the Fox H–function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the G–function, the Fox–Wright function and the Meijer G–function) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory.

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“…The MVRN space (J, Ψ, ) is defined and studied in [21,29]. A triple (J, Ψ, ) is said to be an MVRN space if for each χ, χ ′ ∈ J, and ψ > 0, we have (1)…”

Section: Random Normed (Mvrn) Spacesmentioning

confidence: 99%

Section: Fractional-order Delayed Matrix Sine and Cosinementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Aderyani,

Saadati,

O’Regan

et al. 2024

Mathematics

Self Cite

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“…For the special case of multiple stability, i.e., Mittag-Leffler-Gauss-Hypergeometric-Bessel-Maitland-Fox stability, Mittag-Leffler-Supertrigonometric stability, Mittag-Leffler-Superhyperbolic stability and the others, we refer the reader to [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Best Decision-Making on the Stability of the Smoke Epidemic Model via Z-Numbers and Aggregate Special Maps

O’Regan,

Aderyani,

Saadati

2024

Mathematics

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The present paper considers a fractional-order smoke epidemic model. We apply fuzzy systems and probability theory to make the best decision on the stability of the smoking epidemic model by using a new class of controllers powered by special functions to effectively generalize Ulam-type stability problems. Evaluation of optimal controllability and maximal stability is the new issue. This different concept of stability not only covers the old concepts but also investigates the optimization of the problem. Finally, we apply a new optimal method for the governing model with the Atangana–Baleanu–Caputo fractional derivative to obtain stability results in Banach spaces.

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Introduction

Rezaei Aderyani,

Saadati,

et al. 2024

Studies in Systems, Decision and Control

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Multi-stability of non homogenous vector-valued fractional differential equations in matrix-valued Menger spaces

Cited by 19 publications

References 20 publications

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Best Decision-Making on the Stability of the Smoke Epidemic Model via Z-Numbers and Aggregate Special Maps

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