Convergence and stability analysis of a novel iteration method for fractional biological population equation

We put into action new analytical technique for solving nonlinear fractional partial differential equations arising in biological population dynamics system. We present in details the stability, the convergence, and the uniqueness analysis by constructing a suitable Hilbert space. Some exact analytical solutions are given, and a quantity of properties gives you an idea about signs of biologically practical reliance on the parameter values. The regularity of this course of action and the diminution in computations confer a wider applicability. In all examples, in the limit of infinitely, many terms of the series solution yield the exact solution.

[1]  Guy Jumarie,et al.  On the representation of fractional Brownian motion as an integral with respect to (dt)alpha , 2005, Appl. Math. Lett..

[2]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

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

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

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

[6]  Abdon Atangana,et al.  The Time-Fractional Coupled-Korteweg-de-Vries Equations , 2013 .

[7]  Abdon Atangana,et al.  Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller-Segel equations , 2013 .

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

[9]  Shaowei Wang,et al.  Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus , 2009 .

[10]  G. Jumarie,et al.  Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results , 2006, Comput. Math. Appl..

[11]  Eric Renshaw.  Modelling biological populations in space and time: References , 1991 .

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

[13]  M. Caputo.  Linear models of dissipation whose Q is almost frequency independent , 1966 .

[14]  Mehdi Dehghan,et al.  Numerical solution of a biological population model using He's variational iteration method , 2007, Comput. Math. Appl..

[15]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[16]  Mehmet Merdan,et al.  Numerical solution of time‐fraction modified equal width wave equation , 2012 .

[17]  A. Kılıçman,et al.  Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method , 2013 .

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