HE–ELZAKI METHOD FOR SPATIAL DIFFUSION OF BIOLOGICAL POPULATION

The foremost purpose of this paper is to present a valuable numerical procedure constructed on Elzaki transform and He’s Homotopy perturbation method (HPM) for nonlinear partial differential equation arising in spatial flow characterizing the general biological population model for animals. The actions are made usually by mature animals driven out by intruders or by young animals just accomplished maturity moving out of their parental region to initiate breeding region of their own. He–Elzaki method is a blend of Elzaki transform and He’s HPM. The results attained are compared with Sumudu decomposition method (SDM). The numerical results attained by suggested method specify that the procedure is easy to implement and precise. These outcomes reveal that the proposed method is computationally very striking.

[1]  Emad A.-B. Abdel-Salam,et al.  Analytical solution of nonlinear space–time fractional differential equations using the improved fractional Riccati expansion method , 2015 .

[2]  Juan J. Nieto,et al.  Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions , 2017, Commun. Nonlinear Sci. Numer. Simul..

[3]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[4]  Arzu Akbulut,et al.  Auxiliary equation method for time-fractional differential equations with conformable derivative , 2017, Comput. Math. Appl..

[5]  Abdul-Majid Wazwaz,et al.  The variational iteration method for solving linear and nonlinear systems of PDEs , 2007, Comput. Math. Appl..

[6]  Arturo Sarmiento-Reyes,et al.  Laplace transform–homotopy perturbation method with arbitrary initial approximation and residual error cancelation , 2017 .

[7]  Richard L. Magin,et al.  On the fractional signals and systems , 2011, Signal Process..

[8]  Yu Zhang,et al.  An efficient analytical method for solving local fractional nonlinear PDEs arising in mathematical physics , 2016 .

[9]  Fevzi Erdogan,et al.  Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method , 2016 .

[10]  G. Adomian.  Solution of coupled nonlinear partial differential equations by decomposition , 1996 .

[11]  J. Prakash,et al.  Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method , 2016 .

[12]  Ahmet Bekir,et al.  A novel analytical method for time-fractional differential equations , 2016 .

[13]  Lourenco Beirao da Veiga,et al.  Stability Analysis for the Virtual Element Method , 2016, 1607.05988.

[14]  Boming Yu,et al.  FRACTAL ANALYSIS OF FLOW RESISTANCE IN TREE-LIKE BRANCHING NETWORKS WITH ROUGHENED MICROCHANNELS , 2017 .

[15]  P. Michel.  Large population and size scale limit of a stochastic particle model , 2017 .

[16]  S. Reutskiy.  A new semi-analytical collocation method for solving multi-term fractional partial differential equations with time variable coefficients , 2017 .

[17]  J. Machado,et al.  EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN , 2017 .

[18]  S. Namasivayam,et al.  Natural frequencies of thin rectangular plates using homotopy-perturbation method , 2017 .

[19]  P. Prakash,et al.  Exact solutions and maximal dimension of invariant subspaces of time fractional coupled nonlinear partial differential equations , 2017, Commun. Nonlinear Sci. Numer. Simul..

[20]  D. O’Regan,et al.  On recent developments in the theory of abstract differential equations with fractional derivatives , 2010 .

[21]  Mohamed S. M. Bahgat,et al.  Numerical approaches to system of fractional partial differential equations , 2017 .

[22]  Barkai,et al.  From continuous time random walks to the fractional fokker-planck equation , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Zaid M. Odibat,et al.  Analytic study on linear systems of fractional differential equations , 2010, Comput. Math. Appl..

[24]  M. Şenol,et al.  On the Perturbation–Iteration Algorithm for fractional differential equations , 2016 .

[25]  Tamer A. Abassy.  Improved Adomian decomposition method , 2010, Comput. Math. Appl..

[26]  Mujeeb ur Rehman,et al.  Haar wavelet Picard method for fractional nonlinear partial differential equations , 2015, Appl. Math. Comput..

[27]  D. Lu,et al.  NUMERICAL INVESTIGATION OF FRACTIONAL HIV MODEL USING ELZAKI PROJECTED DIFFERENTIAL TRANSFORM METHOD , 2018, Fractals.

[28]  Qingbiao Wu,et al.  A Novel Technique to Solve Space and Time Fractional Telegraph Equation , 2016 .

[29]  O. Iyiola,et al.  Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations , 2014 .

[30]  E. Maré,et al.  Homotopy perturbation transform method for pricing under pure diffusion models with affine coefficients , 2018 .

[31]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[32]  Atif A. Hemeda,et al.  Modified Homotopy Perturbation Method for Solving Fractional Differential Equations , 2014, J. Appl. Math..

[33]  N. Taghizadeh,et al.  Application of the simplest equation method to some time-fractional partial differential equations , 2013 .

[34]  F. Mainardi.  Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[35]  Hossein Jafari,et al.  A new approach for solving a system of fractional partial differential equations , 2013, Comput. Math. Appl..

[36]  H. Srivastava,et al.  Non-Differentiable Exact Solutions for the Nonlinear ODEs Defined on Fractal Sets , 2017 .

[37]  Jun Wang,et al.  (N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations , 2017, Commun. Nonlinear Sci. Numer. Simul..

[38]  A. Naveed,et al.  New Application of Elzaki Projected Differential Transform Method , 2017 .

[39]  Fawang Liu,et al.  Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation , 2016 .

[40]  Liancun Zheng,et al.  Numerical method to initial-boundary value problems for fractional partial differential equations with time-space variable coefficients , 2016 .

[41]  Xiaoyun Jiang,et al.  Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition , 2009, Appl. Math. Comput..

[42]  F. A. Chandio,et al.  ELZAKI PROJECTED DIFFERENTIAL TRANSFORM METHOD FOR FRACTIONAL ORDER SYSTEM OF LINEAR AND NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATION , 2018 .

[43]  S. Momani,et al.  Solving systems of fractional differential equations using differential transform method , 2008 .

[44]  K. Vishal,et al.  Solution of the nonlinear fractional diffusion equation with absorbent term and external force , 2011 .