An Explication of Finite-Time Stability for Fractional Delay Model with Neutral Impulsive Conditions

Kaliraj, K.; Priya, P. K. Lakshmi; Ravichandran, C.

doi:10.1007/s12346-022-00694-8

Cited by 12 publications

(6 citation statements)

References 34 publications

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“…In recent years, many efficient techniques have been used to obtain approximate and analytical solutions for a fractionalorder partial differential equation, including the double Laplace transform method [14], theta-method [15], reproducing kernel function and CrankNicholson difference method [16], finite element method [17], Laplace decomposition method [18], fractional sub equation method [19], MDLTM [20], Fibonacci wavelet method [21]. The authors in [22] explored the investigation of the finite time stability (FTS) of multi-state neutral fractional order systems when subjected to impulsive perturbations and state delays. The non-local fractional differential equation of the Sobolev type with impulsive conditions was addressed in [23], and the existence and uniqueness of mild solutions using the Banach fixed point technique and analytic semigroup were examined in every approximate solution.…”

Section: Introductionmentioning

confidence: 99%

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Abdulazeez

Modanlı

2023

International Journal of Mathematics and Computer in Engineering

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The Pseudo-Hyperbolic Telegraph partial differential equation (PHTPDE) based on the Caputo fractional derivative is investigated in this paper. The modified double Laplace transform method (MDLTM) is constructed for the proposed model. The MDLTM was used to obtain the analytic solution for the pseudo-hyperbolic telegraph equation of fractional order defined by the Caputo derivative. The proposed method is a highly effective analytical method for the fractional-order pseudo-hyperbolic telegraph equation. A test problem was presented as an example. Based on the results, it is clear that this method is more convenient and produces an analytic solution in fewer steps than other methods that require more steps to have an identical analytical solution. This paper claims to provide an analytic solution to the fractional order pseudohyperbolic telegraph equation using the MDLTM. An analytical solution directs to an exact, closed-form solution that can be expressed in mathematical functions or known operations. Obtaining analytic solutions to PDEs is often challenging, especially for fractional order equations, making this achievement noteworthy.

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Section: Introductionmentioning

confidence: 99%

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Abdulazeez

Modanlı

2023

International Journal of Mathematics and Computer in Engineering

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“…The reason behind the evolution of this particular field is due to the enormous real-life applications such as in modeling the growth of population, networking, fractal theory, fluid dynamics, polymer rheology, neural network, viscoelastic, electrodynamics, earthquake, diffusion in porous media, traffic flow and theory of population dynamics. To gain more knowledge about fractional-order differential systems, one can refer to [1][2][3][4][5][6][7][8][9][10][11] and the articles [12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Existence of solution for Volterra–Fredholm type stochastic fractional integro‐differential system of order μ ∈ (1, 2) with sectorial operators

Kaliraj

Muthuvel

2023

Math Methods in App Sciences

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The mainspring of the study is to investigate the out‐turn of stochastic Volterra–Fredholm integro‐differential inclusion of order μ∈false(1,2false)$$ \mu \in \left(1,2\right) $$ with sectorial operator of the type false(P,η,ϱ,γfalse)$$ \left(P,\eta, \varrho, \gamma \right) $$. The existence results of our proposed problem is derived by employing Martelli's fixed point approach. We do not limit the theoretical results of fractional stochastic equation to local condition but extend to nonlocal condition, and physical interpretation of our obtained results is proved with an appropriate illustration.

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“…Many academics have recently considered the exact and approximate controllability of *Corresponding Author systems characterized by impulsive functional inclusions, integro-differential equations, semilinear functional equations, neutral functional differential equations, and evolution inclusions, to name a few examples, see [23,24,27] and references in that. In [28][29][30][31][32][33][34] Ravi et. al.…”

Section: Introductionmentioning

confidence: 99%

A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

Pandey¹,

Shukla²,

Shukla³

et al. 2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis of this paper. We use fractional calculus, Gronwall's inequality, semigroup theory, and the Cauchy sequence to examine the main results for the proposed system. The application of well-known fixed point theorem methodologies is avoided in this paper. Finally, a fractional heat equation is discussed as an example.

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An Explication of Finite-Time Stability for Fractional Delay Model with Neutral Impulsive Conditions

Cited by 12 publications

References 34 publications

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method

Existence of solution for Volterra–Fredholm type stochastic fractional integro‐differential system of order μ ∈ (1, 2) with sectorial operators

A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

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