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Open accessJournal ArticleDOI: 10.1142/S0218348X21400120

On the approximate solutions for a system of coupled korteweg–de vries equations with local fractional derivative

04 Mar 2021-Fractals (World Scientific Publishing Company)-Vol. 29, Iss: 05, pp 2140012
Abstract: In this paper, we utilize local fractional reduced differential transform (LFRDTM) and local fractional Laplace variational iteration methods (LFLVIM) to obtain approximate solutions for coupled Kd...

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6 results found


Open accessJournal ArticleDOI: 10.22075/IJNAA.2021.5094
Abstract: The Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper.The current technique incorporates two notable strategies in particular Sumudu transform (ST) and homotopy perturbation method (HPM). The proposed method’s hybrid property decreases the number of the quantity of computations and materials needed. In this method, illustration examples evaluate the accuracy and applicability of the mentioned procedure. The outcomes got by FSHPM are in acceptable concurrence with the specific arrangement of the problem.

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2 Citations


Open accessJournal ArticleDOI: 10.3390/MATH9060673
22 Mar 2021-
Abstract: In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined. The iteration transform method solutions are obtained in series form to analyze the analytical results of fractional-order coupled Korteweg-de Vries equations. To understand the analytical procedure of Iteration transform method, some numerical problems are presented for the analytical result of fractional-order coupled Korteweg-de Vries equations. It is also demonstrated that the current technique’s solutions are in good agreement with the exact results. The numerical solutions show that only a few terms are sufficient for obtaining an approximate result, which is efficient, accurate, and reliable.

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1 Citations


Open accessJournal ArticleDOI: 10.22075/IJNAA.2021.4936
Abstract: In this paper, we investigate solutions of nonlinear fractional differential equations by using Natural homotopy perturbation method (NHPM). This method is coupled by the Natural transform (NT) and homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the presented method.

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Topics: Nonlinear system (57%)

1 Citations



Open accessJournal ArticleDOI: 10.1007/S40819-021-01145-9
Abstract: The Nagumo equation describes a reaction–diffusion system in biology. Here, it is coupled to Burgers equation, via including convection, which is the Burgers–Nagumo equation (BNE). The first objective of this work is to present a theorem to reduce, approximately, the different versions of the fractional time derivatives (FTD) to an ordinary derivative (OD) with time dependent coefficients (non autonomous). The second objective is to find the exact solutions of the fractal and FTD-BNE is reduced to BNE with time dependent coefficient. Further similarity transformations are introduced. The unified and extended unified method are used to find the exact traveling waves solutions. Also, self-similar solutions are obtained. The novelties in this work are (i) reducing, via an analytic approximation, the different versions of FTD to non autonomous OD. (ii) Traveling and self-similar waves solutions of the FTD-BNE are derived. (iii) The effect of the order of fractional and fractal derivatives, on waves structure, are investigated. It is found that significant fractal effects hold for smaller order derivatives. While significant fractional effects hold for higher-order derivatives. It is found that, the solutions obtained show solitary wave, wrinkle soliton, solitons with double kinks or with spikes and undulated wave. Further It is shown that wrinkle soliton, with double kink configuration holds for smaller fractal order. While in the case of fractional derivative, this holds for higher orders. We mention that the results found here are completely new. Symbolic computations are carried by using Mathematica.

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Topics: Fractional calculus (59%), Burgers' equation (57%), Time derivative (54%) ... read more

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16 results found


Journal ArticleDOI: 10.1016/J.AMC.2015.10.072
Abstract: The two-dimensional extended differential transform via local fractional derivative is first proposed.The theorems of the two-dimensional extended differential transform method are proved.The numerical solution for the local fractional diffusion equation is considered.The chart of the solution with non-differentiable terms is illustrated. In this article, we first propose a new numerical technique based upon a certain two-dimensional extended differential transform via local fractional derivatives and derive its associated basic theorems and properties. One example of testing the local fractional diffusion equation is then considered. The numerical result presented here illustrates the efficiency and accuracy of the proposed computational technique in order to solve the partial differential equations involving local fractional derivatives.

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122 Citations


Open accessJournal ArticleDOI: 10.1155/2014/170794
Abstract: Copyright © 2014 Yamin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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71 Citations


Open accessJournal ArticleDOI: 10.2298/TSCI120826075L
01 Jan 2013-Thermal Science
Abstract: A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy.

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Topics: Laplace transform (58%), Fractal (56%), Fractional calculus (53%) ... read more

63 Citations


Open accessJournal ArticleDOI: 10.1155/2014/161580
Abstract: We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

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Topics: Fractional calculus (69%), Adomian decomposition method (66%), Laplace's equation (58%) ... read more

55 Citations


Open accessJournal ArticleDOI: 10.1177/1687814016633013
Abstract: The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

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43 Citations