On the approximate solutions for a system of coupled korteweg–de vries equations with local fractional derivative
TL;DR: In this article, local fractional reduced differential transform (LFRDTM) and LFLVIM (local fractional Laplace variational iteration methods) were used to obtain approximate solutions for coupled KdT.
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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22 Mar 2021
TL;DR: 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.
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.
21 citations
TL;DR: In this article , a well-organized and novel algorithm for solving time-fractional Fornberg-Whitham, Klein-Gordon equation and biological population models occurring from physics and engineering is presented.
19 citations
TL;DR: In this paper , a new local fractional method pertaining to the Local fractional Sumudu Transform (LFST) was proposed for computational study of LFSEs.
11 citations
TL;DR: In this article , a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs) was shown using the Gronwall inequality, and the innovative aspect of the proposed study is the application of fixed point theory to show the FTS.
Abstract: This work deals with a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs). In light of this, FTSs of NFOTSs are demonstrated in the literature using the Gronwall inequality. The innovative aspect of our proposed study is the application of fixed point theory to show the FTS of NFOTSs. Finally, using two examples, the theoretical contributions are confirmed and substantiated.
9 citations
TL;DR: In this article, the Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper, the results obtained by FSHPM are in acceptable concurrence with the specific arrangement of the problem.
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.
6 citations
Cites methods from "On the approximate solutions for a ..."
...[5, 6, 7, 8, 9], fractional differential transform method [10, 11, 12], fractional series expansion method [13, 14], fractional Sumudu variational iteration method [15, 16], fractional Laplace transform method [17], fractional homotopy perturbation method [18], fractional Sumudu decomposition method [19, 20, 21], fractional Fourier series method [22], fractional reduced differential transform method [23, 24, 25], fractional Adomian decomposition method [26, 27, 28, 29], and another methods [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]....
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References
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TL;DR: 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.
137 citations
TL;DR: In this article, a reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang Laplace transform and the identification of fractal Lagrange multiplier is investigated.
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.
72 citations
TL;DR: Wang et al. as discussed by the authors presented 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.
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.
71 citations
TL;DR: In this paper, a comparison between the local fractional Adomian decomposition (LFAAD) and LFAFL decomposition was performed for solving the Laplace equation. But the results illustrate the significant features of the two methods which are both very effective and straightforward for solving differential equations with local fractionals derivative.
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.
68 citations
01 Jul 2020
TL;DR: In this paper, the invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives.
Abstract: In this work, the well known invariant subspace method has been modified and extended to solve some partial differential
equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives. The exact solutions are obtained by solving the reduced systems of constructed fractional differential equations. The results show that this method is very simple and effective for constructing explicit exact solutions for partial differential equations involving new fractional derivatives with nonlocal and non-singular kernels, such solutions are very useful to validate new numerical methods
constructed for solving partial differential equations with CF and AB fractional derivatives.
59 citations