Analysis of positive fractional-order neutral time-delay systems

Huseynov, Ismail T.; Mahmudov, Nazım I.

doi:10.1016/j.jfranklin.2021.07.001

Cited by 18 publications

(18 citation statements)

References 23 publications

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“…Furthermore, Medved and Pospisil 21 have derived sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations using multidelay exponential functions via Pinto's inequality. In fractional‐order sense, Huseynov and Mahmudov 19 have established the closed‐form representation of a solution for linear matrix coefficient systems of the Caputo‐type fractional‐order neutral differential equations with two incommensurate constant delays. Moreover, Mahmudov 20 has proposed an explicit analytical solution to linear Riemann–Liouville‐type fractional multidelay differential equations of order l − 1 < α ≤ l for

l \in ℕ

.…”

Section: Introductionmentioning

confidence: 99%

“…Liang et al 17 have investigated the finite‐time stability of linear delay differential equations system via the delayed matrix cosine and sine of polynomial degrees and extended to the same issue of delayed differential equations system with nonlinearity by virtue of Gronwall's inequality approach. Particularly, time‐delay systems with multidelays have a potential to be more suitable for applications in engineering and science 18–21 . Diblik et al 18 have studied nonhomogeneous system of linear differential equations with multiple different delays and pairwise permutable matrices.…”

Section: Introductionmentioning

confidence: 99%

“…Particularly, time-delay systems with multidelays have a potential to be more suitable for applications in engineering and science. [18][19][20][21] Diblik et al 18 have studied nonhomogeneous system of linear differential equations with multiple different delays and pairwise permutable matrices. Furthermore, Medved and Pospisil 21 have derived sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations using multidelay exponential functions via Pinto's inequality.…”

Section: Introductionmentioning

confidence: 99%

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On a study of Sobolev‐type fractional functional evolution equations

Huseynov

Ahmadova

Mahmudov

2022

Math Methods in App Sciences

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Sobolev-type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate the existence of mild solutions for fractional-order time-delay evolution equation of Sobolev type with multiorders in a Banach space with the help of two various methods. First, we study abstract problem by assuming the existence and compactness of E −1 and introduce a closed-form representation of a mild solution via a newly defined delayed Mittag-Leffler-type function which is generated by nonpermutable and permutable linear-bounded operators. Our second method is based on the theory of Sobolev-type delayed resolvent families generated by the pair (A, E) and a subordination principle, and in this case, any restrictive assumptions are not required on E. Furthermore, we derive an exact analytical representation of solutions for multidimensional fractional functional dynamical systems with nonpermutable and permutable matrices. As an example, the Sobolev-type delayed wave equation with a damping term is provided to illustrate the applications of the abstract results.

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l \in ℕ

.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On a study of Sobolev‐type fractional functional evolution equations

Huseynov

Ahmadova

Mahmudov

2022

Math Methods in App Sciences

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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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“…For more general results, using the Laplace transform technique, Mahmudov has proposed in [9], a closed-form representation of solutions for linear delay differential equations using a multiple delayed perturbation of the Mittag-Leffler matrix functions. Moreover, Huseynov and Mahmudov [10] have analyzed linear matrix coefficient systems of the neutral differential equations of integer and fractional orders with two incommensurate constant delays in terms of several aspects: positivity criterion, existence & uniqueness, and stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Construction of solutions for delay evolution equations in a Banach space: A delayed Dyson-Phillips series

Huseynov¹,

Mahmudov²

2021

Preprint

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Functional evolution equations have many applications in modeling many physical processes. First, using the generation theorem, we prove that a fundamental solution of the delay evolution equation is a strongly continuous semigroup of linear operators. Second, we introduce a closed-form representation of a fundamental solution using a delayed Dyson-Phillips series. Then, we establish the analytical representation of the classical solutions of linear homogeneous/nonhomogeneous evolution equations with a discrete delay in a Banach space. In the special case, we consider delay evolution equations with permutable/nonpermutable linear bounded operators and derive crucial results in terms of noncommutative analysis. Furthermore, we prove that a fundamental solution of a functional evolution equation with bounded linear operator coefficients is a uniformly continuous semigroup of linear operators. Finally, we present an example in the context of a one-dimensional heat equation with a discrete delay to demonstrate the applicability of our theoretical results and we give some comparisons with existing results.

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Analysis of positive fractional-order neutral time-delay systems

Cited by 18 publications

References 23 publications

On a study of Sobolev‐type fractional functional evolution equations

On a study of Sobolev‐type fractional functional evolution equations

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

Construction of solutions for delay evolution equations in a Banach space: A delayed Dyson-Phillips series

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