Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform

Thabet, Hayman; Kendre, Subhash

doi:10.1016/j.chaos.2018.03.001

Cited by 78 publications

(37 citation statements)

References 17 publications

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“…Over the past few decades, a simple definition called conformable fractional derivative was proposed in [9]. For more results about conformable fractional derivative, we refer the reader to [10][11][12][13][14][15][16][17][18]. This derivative seems to be more natural, and it coincides with the classical definition of the first derivative.…”

Section: Introductionmentioning

confidence: 92%

Asymptotical stability analysis of conformable fractional systems

Wang

2019

Journal of Taibah University for Science

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Section: Introductionmentioning

confidence: 92%

Asymptotical stability analysis of conformable fractional systems

Wang

2019

Journal of Taibah University for Science

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“…(i) Suppose that h ∈ (-γ 2 4β , 0). Two families of periodic orbits of system (3.18) are defined by the algebraic equation 24) where χ 1h = -γ β -1 β γ 2 + 4βh, χ 2h = -γ β + 1 β γ 2 + 4βh. Integrating them along the periodic orbits, we obtain two families of periodic traveling wave solutions, namely (iii) Suppose that h ∈ (0, +∞).…”

Section: Bifurcation Phase Portraits and Exact Solutions For Equatimentioning

confidence: 99%

“…Recently, Khalil and coworkers [21] introduced the conformable fractional derivative. After that, some scholars [22][23][24][25] have begun to discuss the exact solutions of FPDEs in the sense of the conformable fractional derivative. In this paper, we will introduce the procedure of the generalized (G /G)expansion method for FPDEs, and will discuss the exact traveling wave solutions of the (2 + 1)-dimensional conformable time-fractional Zoomeron equation by the generalized (G /G)-expansion method together with conformable fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and exact solutions for the ($2+1$)-dimensional conformable time-fractional Zoomeron equation

Han

2020

Adv Differ Equ

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In this paper, the bifurcation and new exact solutions for the ($2+1$ 2 + 1 )-dimensional conformable time-fractional Zoomeron equation are investigated by utilizing two reliable methods, which are generalized $(G'/G)$ ( G ′ / G ) -expansion method and the integral bifurcation method. The exact solutions of the ($2+1$ 2 + 1 )-dimensional conformable time-fractional Zoomeron equation are obtained by utilizing the generalized $(G'/G)$ ( G ′ / G ) -expansion method, these solutions are classified as hyperbolic function solutions, trigonometric function solutions, and rational function solutions. Giving different parameter conditions, many integral bifurcations, phase portraits, and traveling wave solutions for the equation are obtained via the integral bifurcation method. Graphical representations of different kinds of the exact solutions reveal that the two methods are of significance for constructing the exact solutions of fractional partial differential equation.

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“…Since then, several studies have appeared in the literature. For more details see [26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Adaptation of Conformable Residual Power Series Scheme in Solving Nonlinear Fractional Quantum Mechanics Problems

et al. 2020

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In this paper, the general state of quantum mechanics equations that can be typically expressed by nonlinear fractional Schrödinger models will be solved based on an attractive efficient analytical technique, namely the conformable residual power series (CRPS). The fractional derivative is considered in a conformable sense. The desired analytical solution is obtained using conformable Taylor series expansion through substituting a truncated conformable fractional series and minimizing its residual errors to extract a supportive approximate solution in a rapidly convergent fractional series. This adaptation can be implemented as a novel alternative technique to deal with many nonlinear issues occurring in quantum physics. The effectiveness and feasibility of the CRPS procedures are illustrated by verifying three realistic applications. The obtained numerical results and graphical consequences indicate that the suggested method is a convenient and remarkably powerful tool in solving different types of fractional partial differential models.

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Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform

Cited by 78 publications

References 17 publications

Asymptotical stability analysis of conformable fractional systems

Asymptotical stability analysis of conformable fractional systems

Bifurcation and exact solutions for the ($2+1$)-dimensional conformable time-fractional Zoomeron equation

Adaptation of Conformable Residual Power Series Scheme in Solving Nonlinear Fractional Quantum Mechanics Problems

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