A powerful approach for fractional Drinfeld–Sokolov–Wilson equation with Mittag-Leffler law

Gao, Wei; Veeresha, P.; Prakasha, D. G.; Başkonuş, Hacı Mehmet; Yel, Gülnur

doi:10.1016/j.aej.2019.11.002

Cited by 72 publications

(31 citation statements)

References 48 publications

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“…The next corollary was the main result of the study, giving us conditions of the connection between the pair of limit functions (x * (·, x 0 , y 0 ), y * (·, x 0 , y 0 )) of the sequences (13) and the exact solution of the mixed type FBVP (11), (12).…”

Section: Study Of the Lower Order Fractional Differential Systemsmentioning

confidence: 99%

“…Indeed, in [26] we derived these conditions; i.e., we supposed that the BVP (11), (12) is such that the following conditions hold:…”

Section: Study Of the Lower Order Fractional Differential Systemsmentioning

confidence: 99%

“…A choice of the zero-approximation in the form (22) is optimal in the sense that it improves the estimate of difference between the m-th approximation x m (·, ξ 0 ) and its limit function x ∞ (·, ξ 0 ). In the case of selection x 0 (t, ξ 0 ) = x 0 , as it was for the PFBVPs (5), (6) and (11), (12), it would lead to additional terms in the estimates that would increase the error of computations.…”

Section: Anti-periodic Fractional Bvpmentioning

confidence: 99%

“…During the last few years, a number of papers devoted to the numerical-analytic methods of approximation of solutions of the fractional ordinary and partial differential equations were published. In particular, those were the well known homotopy perturbation method [12][13][14][15], Adomian's decomposition method [16][17][18][19][20][21], the variation iteration method [20,22,23], and the exp-function method [24].…”

Section: Introductionmentioning

confidence: 99%

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On One Interpolation Type Fractional Boundary-Value Problem

Marynets

2020

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We present some new results on the approximation of solutions of a special type of fractional boundary-value problem. The focus of our research is a system of three fractional differential equations of the mixed order, subjected to the so-called “interpolation” type boundary restrictions. Under certain conditions, the aforementioned problem is simplified via a proper parametrization technique, and with the help of the numerical-analytic method, the approximate solutions are constructed.

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Section: Study Of the Lower Order Fractional Differential Systemsmentioning

confidence: 99%

“…Indeed, in [26] we derived these conditions; i.e., we supposed that the BVP (11), (12) is such that the following conditions hold:…”

Section: Study Of the Lower Order Fractional Differential Systemsmentioning

confidence: 99%

Section: Anti-periodic Fractional Bvpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On One Interpolation Type Fractional Boundary-Value Problem

Marynets

2020

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“…In 2015, Caputo and Fabrizio discovered a new operator of arbitrary order, namely, Caputo‐Fabrizio (CF) operator with arbitrary order and enforced to the several linear and nonlinear physical problems . In 2016, Atangana and Baleanu introduced another nonsingular derivative based on Miitag‐Leffler kernel and applied to the many problems . The parabolic heat equation was first developed and introduced Joseph Fourier in 1822.…”

Section: Introductionmentioning

confidence: 99%

An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

Kumar

Ghosh

Samet

et al. 2020

Math Methods in App Sciences

181

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The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional-exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multi dimensional heat equations of arbitrary order by using analytical approach homotopy perturbation transform method and residual power series method, where new fractional operator has been taken in new Yang-Abdel-Aty-Cattani (YAC) sense. The obtained results indicate that solution converges to the original solution in language of generalized Mittag-Leffler function. Three numerical examples are discussed to draw an effective attention to reveal the proficiency and adaptability of the recommended methods on new YAC operator. KEYWORDS HPTM and RPSM, multidimensional heat equations, new fractional derivative, new YAC operator, Prabhakar or generalized Mittag-Leffler function MSC CLASSIFICATION 26A33; 34A08; 34A34; 60G22 Math Meth Appl Sci. 2020;43:6062-6080. wileyonlinelibrary.com/journal/mma

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An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

et al. 2020

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In this paper, the q‐homotopy analysis transform method (q‐HATM) is applied to find the solution for the fractional Lakshmanan‐Porsezian‐Daniel (LPD) model. The LPD model is the generalization of the non‐linear Schrödinger (NLS) equation. The proposed method is graceful fusions of Laplace transform technique with q‐homotopy analysis scheme, and the derivative is considered in Caputo sense. In order to validate and illustrate the efficiency of the proposed method, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured for the three different cases in terms of 3D and contour plots for diverse values of the fractional order. The obtained results confirm that the future method is easy to implement, highly methodical, and very effective to analyse the behaviour of complex non‐linear fractional differential equations exist in the connected areas of science and engineering.

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A powerful approach for fractional Drinfeld–Sokolov–Wilson equation with Mittag-Leffler law

Cited by 72 publications

References 48 publications

On One Interpolation Type Fractional Boundary-Value Problem

On One Interpolation Type Fractional Boundary-Value Problem

An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

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