Residual power series method for fractional Sharma-Tasso-Olever equation

Kumar, Amit; Kumar, Sunil; Singh, M.

doi:10.5899/2016/cna-00235

Cited by 51 publications

(36 citation statements)

References 13 publications

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“…Res(x, t) = 0 and lim k→∞ Res k (x, t) = Res(x, t) for each x ∈ I and 0 ≤ t. In fact this lead to ∂ (n−1)α ∂t (n−1)α Res k (x, t) for n = 1, 2, 3, ..., k because in the conformable sense, the fractional derivative of a constant is zero [4,12,15]. Solving the equation ∂ (n−1)α ∂t (n−1)α Res k (x, 0) = 0 gives us the desired f n (x) coefficients.…”

Section: It Is Clear Thatmentioning

confidence: 99%

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New Exact and Numerical Solutions of Fractional Kaup-Kupershmidt Equation

2019

apjm

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A. In this article, the tanh method and the residual power series method (RPSM) are used to obtain new exact and numerical solutions of the time-fractional Kaup-Kupershmidt equation using the conformable fractional derivative definition. This definition is simple, effective and reliable in the solution procedure of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo and Rieman-Liouville. 2010 Mathematics Subject Classification. 35R11; 35A20; 35C05.

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Section: It Is Clear Thatmentioning

confidence: 99%

“…The tanh method is a powerful tool for obtaining traveling wave solutions of nonlinear fractional differential equations. In this method a power series in tanh was used as an ansatz to obtain analytical solutions of traveling the help of one or more variable algebraic equation chains, and finally, a so-called truncated series solution is obtained [15].…”

mentioning

confidence: 99%

New Exact and Numerical Solutions of Fractional Kaup-Kupershmidt Equation

2019

apjm

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“…According to the RPSM [6,7], by starting with the initial guess approximation u 0,0 (x, t) = 1 + cosh(2x), the series solution of (3.1) can be written in the form…”

Section: Applications Of Rpsm To Schrödinger Equationsmentioning

confidence: 99%

“…Further, this method was effectively used for finding the solution of various kinds of FDEs [2,6,7]. Based on the generalized Taylor series formula method, an approximate analytical solution was given in the form of a convergent series.…”

Section: Introductionmentioning

confidence: 99%

Residual power series method for time-fractional Schrödinger equations

Yu¹,

Kumar²,

Kumar³

et al. 2016

J. Nonlinear Sci. Appl.

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In this paper, the residual power series method (RPSM) is effectively applied to find the exact solutions of fractional-order time dependent Schrödinger equations. The competency of the method is examined by applying it to the several numerical examples. Mainly, we find that our solutions obtained by the proposed method are completely compatible with the solutions available in the literature. The obtained results interpret that the proposed method is very effective and simple for handling different types of fractional differential equations (FDEs).

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“…The FPDEs were adopted to model the thermal science, fluid dynamics, electrical network, chemical physics, optics and so on (see [4,5,13]). Conventionally various technologies, e.g., the Adomian decomposition method (ADM) [6], variation iteration method (VIM) [18], homotopy perturbation method (HPM) [1,15], homotopy decomposition method (HDM) [2], homotopy analysis method (HAM) [11,12,17], residual power series method (RPSM) [8], traveling wave method (TWM) [16], and homotopy analysis Laplace transform method (MHALTM) [7] were used for the solutions of such type of the FPDEs.…”

Section: Introductionmentioning

confidence: 99%

On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method

Li¹,

Kumar²,

Kumar³

et al. 2016

J. Nonlinear Sci. Appl.

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The approximate solution of the time-fractional KdV equation (KdV) by using modified homotopy analysis Laplace transform method, which is a combined form of the Laplace transform and homotopy analysis methods, is investigated for the first time in this article. Comparison of series solutions between under a rapid convergence and the optimal values of convergence parameter is made. The results through the L 2 and L ∞ error norms are also analyzed. The validity, flexibility, and accuracy of the proposed method is conformed through the numerical computations as well as graphical presentations of the results. c 2016 All rights reserved.

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Residual power series method for fractional Sharma-Tasso-Olever equation

Cited by 51 publications

References 13 publications

New Exact and Numerical Solutions of Fractional Kaup-Kupershmidt Equation

New Exact and Numerical Solutions of Fractional Kaup-Kupershmidt Equation

Residual power series method for time-fractional Schrödinger equations

On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method

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