Controllability of fractional stochastic delay dynamical systems

Ahmadova, Arzu; Huseynov, Ismail T.; Mahmudov, Nazım I.

doi:10.48550/arxiv.2009.10654

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…1 The existence and uniqueness problems of FDEs with constant delay and the stability of their solutions are crucial topics in the field of fractional differential equations. Many renowned scientists, such as Ahmed et al, 2 Moniri et al, 3 Vivek et al, 4 Mahmudov et al, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Khusainov et al, 23 Podlubny, 24 and Sousa et al 1,25 have made significant contributions to these problems. 1,[26][27][28][29][30][31][32] In conclusion, fractional differential equations and pseudo-analysis are fascinating areas of research with wide-ranging applications in various fields.…”

Section: Article Pubsaiporg/aip/jmpmentioning

confidence: 99%

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Asadzade,

Mahmudov

2024

Journal of Mathematical Physics

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In this write-up, we focus on pseudo-Hilfer-type fractional order delayed differential equations with bounded definite integral initial conditions on the time interval [0, T]. We begin by establishing relevant lemmas. Then, we derive the solution to the homogeneous Hilfer-type pseudo-fractional order retarded differential equation that satisfies the appropriate initial condition using classical methods. Next, we obtain explicit formulas for solutions to linear inhomogeneous Hilfer-type pseudo-fractional time retarded differential equations with constant coefficients, employing classical ideas. Furthermore, we investigate the existence and uniqueness of the solution of the Hilfer-type pseudo-fractional order delayed differential equation and demonstrate the stability of the given differential equation in the Ulam-Hyers sense on the time interval [0, T].

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Section: Article Pubsaiporg/aip/jmpmentioning

confidence: 99%

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Asadzade,

Mahmudov

2024

Journal of Mathematical Physics

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“…For pure mathematical results, we refer to [37] for existence and uniqueness, Ref. [38][39][40] for stability, and [41] for controllability. For most FDDEs, exact solutions are not known.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

Avcı

2021

Fractal Fract

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In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures.

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“…Several outcomes have been investigated on the qualitative theory and applications of fractional stochastic functional differential equations (FSDEs) [6,14,38,40]. For instance, Mahmudov and McKibben [21] studied the approximate controllability of fractional evolution equations involving generalized Riemann-Liouville fractional derivative in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations

Ahmadova¹,

Mahmudov²

2021

Preprint

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The novelty of our paper is to establish results on asymptotic stability of mild solutions in pth moment to Riemann-Liouville fractional stochastic neutral differential equations (for short Riemann-Liouville FSNDEs) of order α ∈ ( 1 2 , 1) using a Banach's contraction mapping principle. The core point of this paper is to derive the mild solution of FSNDEs involving Riemann-Liouville fractional time-derivative by applying the stochastic version of variation of constants formula. The results are obtained with the help of the theory of fractional differential equations, some properties of Mittag-Leffler functions and asymptotic analysis under the assumption that the corresponding fractional stochastic neutral dynamical system is asymptotically stable.

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Controllability of fractional stochastic delay dynamical systems

Cited by 3 publications

References 23 publications

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis

Asymptotic stability analysis of Riemann-Liouville fractional stochastic neutral differential equations

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