An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations

Odibat, Zaid; Ertürk, Vedat Suat; Kumar, Pushpendra; Makhlouf, Abdellatif Ben; Govindaraj, V.

doi:10.1155/2022/8280203

Cited by 15 publications

(9 citation statements)

References 45 publications

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“…Lemma 2.1. For the coefficients V j k ( ) appeared in (10), one has the following recursive relation…”

Section: Fractional Adams Arrays 21 Fractional Adams-moulton Arraymentioning

confidence: 99%

See 1 more Smart Citation

Higher-order fractional linear multi-step methods

Marasi¹,

Derakhshan²,

Joujehi³

et al. 2023

Phys. Scr.

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In this paper, we propose two arrays, containing the coefficients of fractional Adams-Bashforth and Adams-Moulton methods, and also recursive relations to produce the elements of these arrays. Then, we illustrate the application of these arrays in a suitable way to construct higher-order fractional linear multi-step methods in general form, with extended stability regions. The effectiveness of the new method is shown in comparison with some available previous results in an illustrative test problem.

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“…Lemma 2.1. For the coefficients V j k ( ) appeared in (10), one has the following recursive relation…”

Section: Fractional Adams Arrays 21 Fractional Adams-moulton Arraymentioning

confidence: 99%

“…Some recent works related to the several computational methods to solve various types of fractional-order differential equations can be seen in ref. [8][9][10][11]. In [12], the authors proposed some novel analyses of multistep methods for fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Higher-order fractional linear multi-step methods

Marasi¹,

Derakhshan²,

Joujehi³

et al. 2023

Phys. Scr.

Self Cite

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“…In [28], the authors have explored the new versions of Euler and Runge-Kutta schemes using a non-uniform grid in terms of the generalized Caputo derivative. In [29], the derivation of a generalized differential transform method for impulsive FDEs has been proposed.…”

Section: Introductionmentioning

confidence: 99%

A new numerical method to solve fractional differential equations in terms of Caputo-Fabrizio derivatives

Mahatekar¹,

Scindia²,

Kumar

2023

Phys. Scr.

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In this article, we derive a new numerical method to solve fractional differential equations containing Caputo-Fabrizio derivatives. The fundamental concepts of fractional calculus, numerical analysis, and fixed point theory form the basis of this study. Along with the derivation of the algorithm of the proposed method, error and stability analyses are performed briefly. To explore the validity and effectiveness of the proposed method, several examples are simulated, and the new solutions are compared with the outputs of the previously published two-step Adams-Bashforth method.

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“…Tese derivatives have many uses and properties. For example, they are used to extend Newton mechanics [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Existence of a Unique Solution and the Hyers–Ulam‐H‐Fox Stability of the Conformable Fractional Differential Equation by Matrix‐Valued Fuzzy Controllers

et al. 2022

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In this paper, we consider a conformable fractional differential equation with a constant coefficient and obtain an approximation for this equation using the Radu–Mihet method, which is derived from the alternative fixed- point theorem. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers–Ulam-H-Fox stability for this equation. Finally, by providing numerical examples, we show the application of the obtained results.

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An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations

Cited by 15 publications

References 45 publications

Higher-order fractional linear multi-step methods

Higher-order fractional linear multi-step methods

A new numerical method to solve fractional differential equations in terms of Caputo-Fabrizio derivatives

Existence of a Unique Solution and the Hyers–Ulam‐H‐Fox Stability of the Conformable Fractional Differential Equation by Matrix‐Valued Fuzzy Controllers

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