Computational Analysis of Complex Population Dynamical Model with Arbitrary Order

This paper considers the approximation of solution for a fractional order biological population model. The fractional derivative is considered in the Caputo sense. By using Laplace Adomian decomposition method (LADM), we construct a base function and provide deformation equation of higher order in a simple equation. The considered scheme gives us a solution in the form of rapidly convergent infinite series. Some examples are used to show the efficiency of the method. The results show that LADM is efficient and accurate for solving such types of nonlinear problems.

[1]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

[2]  D. Ganji.  The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer , 2006 .

[3]  Dumitru Baleanu,et al.  A Central Difference Numerical Scheme for Fractional Optimal Control Problems , 2008, 0811.4368.

[4]  Saad Zagloul Rida,et al.  GENERAL: Exact Solutions of Fractional-Order Biological Population Model , 2009 .

[5]  Majid Khan,et al.  Application of Laplace decomposition method on semi-infinite domain , 2011, Numerical Algorithms.

[6]  Jafar Biazar,et al.  Extracting a general iterative method from an Adomian decomposition method and comparing it to the variational iteration method , 2010, Comput. Math. Appl..

[7]  Saad Zagloul Rida,et al.  Homotopy Analysis Method for Solving Biological Population Model , 2011 .

[8]  H. Kheiri,et al.  HOMOTOPY ANALYSIS AND HOMOTOPY PADE METHODS FOR THE MODIFIED BURGERS-KORTEWEG-DE VRIES AND THE NEWELL -WHITEHEAD EQUATIONS , 2011 .

[9]  An Efficient Numerical Method for Solving Linear and Nonlinear Partial Differential Equations by Combining Homotopy Analysis and Transform Method , 2011 .

[10]  Yasir Khan,et al.  Homotopy perturbation transform method for nonlinear equations using He's polynomials , 2011, Comput. Math. Appl..

[11]  Iqtadar Hussain,et al.  A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi infinite domain , 2012, Math. Comput. Model..

[12]  Habibolla Latifizadeh.  APPLICATION OF HOMOTOPY ANALYSIS TRANSFORM METHOD TO FRACTIONAL BIOLOGICAL POPULATION MODEL , 2013 .

[13]  A. Atangana,et al.  New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model , 2016, 1602.03408.

[14]  F. Haq,et al.  Existence and Uniqueness of Positive Solution to Boundary Value Problem of Fractional Differential Equations , 2016 .

[15]  F. Haq,et al.  Numerical analysis of fractional order model of HIV-1 infection of CD4+ T-cells , 2017 .

[16]  Ghaus ur Rahman,et al.  Numerical solution of fractional order smoking model via laplace Adomian decomposition method , 2017, Alexandria Engineering Journal.