Fractional variational iteration method for solving time-fractional Newell-Whitehead-Segel equation

Abstract In this paper, Newell–Whitehead–Segel equations of fractional order are solved by fractional variational iteration method. Convergence analysis and numerical examples are presented to show the efficiency of the proposed numerical method. Plotted graph demonstrate the mightiness and accurateness of the proposed technique.

[1]  John Whitehead,et al.  Finite bandwidth, finite amplitude convection , 1969, Journal of Fluid Mechanics.

[2]  Devendra Kumar,et al.  Fractional modelling arising in unidirectional propagation of long waves in dispersive media , 2016 .

[3]  R. Sharma,et al.  Numerical approximation of Newell-Whitehead-Segel equation of fractional order , 2016 .

[5]  Sunil Kumar,et al.  An efficient computational approach for time-fractional Rosenau–Hyman equation , 2017, Neural Computing and Applications.

[6]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[7]  S. Bhalekar,et al.  Approximate analytical solutions of Newell-Whitehead-Segel equation using a new iterative method , 2015 .

[8]  M. G. Sakar,et al.  Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation , 2015 .

[9]  Z. Hammouch,et al.  Approximate analytical solution to a time-fractional Zakharov-Kuznetsov equation , 2013 .

[10]  The Approximate Solution of Newell Whitehead Segel and Fisher Equations Using The Adomian Decomposition Method , 2016, 1602.04084.

[11]  Manoj Kumar,et al.  Numerical method for solving time-fractional multi-dimensional diffusion equations , 2017, Int. J. Comput. Sci. Math..

[12]  Amit Prakash,et al.  Analytical method for space-fractional telegraph equation by homotopy perturbation transform method , 2016 .

[13]  P. Pue-on.  Laplace Adomian Decomposition Method for Solving Newell-Whitehead-Segel Equation , 2013 .

[14]  Mehdi Dehghan,et al.  On the convergence of He's variational iteration method , 2007 .

[15]  S. Momani,et al.  Numerical methods for nonlinear partial differential equations of fractional order , 2008 .

[16]  Approximate Analytical and Numerical Solutions to Fractional KPP-like Equations , 2013 .

[17]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[18]  Jorge Eduardo Macías-Díaz,et al.  A non-standard symmetry-preserving method to compute bounded solutions of a generalized Newell-Whitehead-Segel equation , 2011 .

[19]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[20]  Amit Kumar,et al.  A Modified Analytical Approach for Fractional Discrete KdV Equations Arising in Particle Vibrations , 2018 .

[21]  Amit Kumar,et al.  A nonlinear fractional model to describe the population dynamics of two interacting species , 2017 .

[22]  Hossein Jafari,et al.  Homotopy analysis method for solving multi-term linear and nonlinear diffusion-wave equations of fractional order , 2010, Comput. Math. Appl..

[23]  Amit Prakash,et al.  Numerical solution of two dimensional time fractional-order biological population model , 2016 .

[24]  Manoj Kumar,et al.  Numerical method for fractional dispersive partial differential equations , 2017 .

[25]  Sunil Kumar,et al.  A new analysis for the Keller-Segel model of fractional order , 2017, Numerical Algorithms.

[26]  Zaid M. Odibat,et al.  A study on the convergence of variational iteration method , 2010, Math. Comput. Model..

[27]  Manoj Kumar,et al.  Numerical method for solving fractional coupled Burgers equations , 2015, Appl. Math. Comput..

[28]  I. Podlubny.  Fractional differential equations , 1998 .

[29]  Y. Cherruault,et al.  New ideas for proving convergence of decomposition methods , 1995 .

[30]  Abdul-Majid Wazwaz,et al.  A new algorithm for calculating adomian polynomials for nonlinear operators , 2000, Appl. Math. Comput..

[31]  H. Jassim.  Homotopy perturbation algorithm using Laplace transform for Newell-Whitehead-Segel equation , 2015 .

[32]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[33]  D. Baleanu,et al.  ON THE FRACTIONAL-ORDER DIFFUSION-WAVE PROCESS , 2010 .

[34]  Amit Prakash,et al.  HE'S VARIATIONAL ITERATION METHOD FOR THE SOLUTION OF NONLINEAR NEWELL-WHITEHEAD-SEGEL EQUATION , 2016 .

[35]  Devendra Kumar,et al.  Homotopy Analysis Sumudu Transform Method for Nonlinear Equations , 2012 .

[36]  Aytac Arikoglu,et al.  Solution of fractional differential equations by using differential transform method , 2007 .

[37]  Hardish Kaur,et al.  Numerical solution for fractional model of Fokker-Planck equation by using q-HATM , 2017 .

[38]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[39]  Yinnian He,et al.  Homotopy analysis method for higher-order fractional integro-differential equations , 2011, Comput. Math. Appl..

[40]  Ji-Huan He,et al.  Variational iteration method: New development and applications , 2007, Comput. Math. Appl..

[41]  A. Saravanan,et al.  A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell–Whitehead–Segel equation , 2013 .