An analytic algorithm for time fractional nonlinear reaction–diffusion equation based on a new iterative method

Baranwal, Vipul K.; Pandey, Ram K.; Tripathi, Manoj P.; Singh, Om Prakash

doi:10.1016/j.cnsns.2012.02.015

Cited by 26 publications

(26 citation statements)

References 27 publications

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“…These results are obtained using RPSM and an NIM. 22 This table clarifies the convergence of the approximate solutions to the exact solution, and exact error is being smaller as the value of the t is decreasing.…”

Section: Basic Definitions Of Fractional Calculus Theorymentioning

confidence: 80%

“…These results are obtained using RPSM, HAM, 21 FVIM, 24 and an NIM. 22 These table clarify the exact error is being smallest in the value of the t = 0:01. Example 2.…”

Section: Basic Definitions Of Fractional Calculus Theorymentioning

confidence: 81%

“…If we write r(u) = u 2 (1 À u) and K = 1=2, equation (2) leads to two-dimensional time fractional Fisher equation. 22 This equations are as follows…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solutions of the time fractional reaction–diffusion equations with residual power series method

Tchier

İnç

Körpınar

et al. 2016

Advances in Mechanical Engineering

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In this article, the residual power series method for solving nonlinear time fractional reaction-diffusion equations is introduced. Residual power series algorithm gets Maclaurin expansion of the solution. The algorithm is tested on Fitzhugh-Nagumo and generalized Fisher equations with nonlinearity ranging. The solutions of our equation are computed in the form of rapidly convergent series with easily calculable components using Mathematica software package. Reliability of the method is given by graphical consequences, and series solutions are used to illustrate the solution. The found consequences show that the method is a powerful and efficient method in determination of solution of the time fractional reaction-diffusion equations.

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Section: Basic Definitions Of Fractional Calculus Theorymentioning

confidence: 80%

“…These results are obtained using RPSM, HAM, 21 FVIM, 24 and an NIM. 22 These table clarify the exact error is being smallest in the value of the t = 0:01. Example 2.…”

Section: Basic Definitions Of Fractional Calculus Theorymentioning

confidence: 81%

See 1 more Smart Citation

Solutions of the time fractional reaction–diffusion equations with residual power series method

Tchier

İnç

Körpınar

et al. 2016

Advances in Mechanical Engineering

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show abstract

“…The RPSM was established as an powerful method for fuzzy differential equations [17]. It has been successfully applied in various fields [18][19][20][21][22][23][24][25][26][27][28][29]. The solution of problems by RPSM are obtained in the form of Maclaurin series.…”

Section: Introductionmentioning

confidence: 99%

On time-fractional Lotka-Volterra diffusion model

Demir¹,

Bayrak²

2019

ntmsci

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The interest of this paper to find the solution of time-fractional Lotka-Volterra diffusion problem by implementing the residual power series method (RPSM). The fractional derivative is described in the Caputo sense. The desired solution of the nonlinear equations are established in the form of rapidly convergent series whose components are computed by Matlab Software Package. The obtained results and graphical consequences show that the suggested method in this study is very efficient, effective and reliable for the solution of the time-fractional Lotka-Volterra equation.

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“…Sungu and Demir 23 applied generalized differential transform and finite difference method for numerical solutions of the equation. Baranwal et al 26 and Merdan 27 used fractional variational iteration method for series solutions of proposed equation.…”

Section: Introductionmentioning

confidence: 99%

A new iterative algorithm on the time-fractional Fisher equation: Residual power series method

Qurashi

Körpınar

Băleanu

et al. 2017

Advances in Mechanical Engineering

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In this article, the residual power series method is used to solve time-fractional Fisher equation. The residual power series method gets Maclaurin expansion of the solution. The solutions of present equation are computed in the shape of quickly convergent series with quickly calculable fundamentals using mathematica software package. Explanation of the method is given by graphical consequences and series solutions are made use of to represent our solution. The found consequences show that technique is a power and efficient method in conviction of solution time-fractional Fisher equation.

show abstract

An analytic algorithm for time fractional nonlinear reaction–diffusion equation based on a new iterative method

Cited by 26 publications

References 27 publications

Solutions of the time fractional reaction–diffusion equations with residual power series method

Solutions of the time fractional reaction–diffusion equations with residual power series method

On time-fractional Lotka-Volterra diffusion model

A new iterative algorithm on the time-fractional Fisher equation: Residual power series method

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