Numerical solution of two dimensional time fractional-order biological population model

Abstract

Abstract:In this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional order α.

A reliable algorithm for time-fractional Navier-Stokes equations via Laplace transform

“…The most important among such models are those described by arbitrary order PDEs. Adomian decomposition [1], homotopy analysis, residual power series, fractional reduced differential transform, fractional variational iteration method [2][3][4], Laplace homotopy technique [5], Laplace variational iteration method [6], homotopy perturbation transform method [7], q-homotopy analysis transform method [8][9][10], modified trial equation method [11], new iterative Sumudu transform method [12] and Laplace perturbation method [13] etc. are some impor-tant methods which are applied to find numerical solution of these problems.…”

Analysis of an Epidemic Spreading Model with Exponential Decay Law

“…Finally, they have supported their theoretical aspects with a numerical example. In addition to these studies, in the literature there are many papers demonstrate to model other epidemic models and special diseases such as modelling the spread of computer virus [9], stability analysis of a fractional human African trypanosomiasis model [10], a schistosomiasis disease model [11], a novel framework for blood vessels detection in retinal images [12], a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model [13], SIRI epidemic model with distributed delay and relapse [14], etc.…”

A reliable numerical algorithm for a fractional model of Fitzhugh-Nagumo equation arising in the transmission of nerve impulses

“…Fractional partial di erential equations are an important class of di erential equations as the fractional calculus operators are nonlocal operators and are suitable to describe the nonlocal e ects characterizing most of the real-world phenomena. Many vigorous methods have been constructed for solving fractional di erential equations such as homotopy perturbation method [1], qhomotopy analysis transform method [2], new iterative Sumudu transform method [3], reduced di erential transform method [4], nite element method [5], operational matrix method [6], Adomian decomposition method [7], variational iteration method [8][9][10][11][12] and many more. In [13], W. P. Bu and A. G. Xiao have developed a novel test basis function for the Petrov-Galerkin nite element method to solve one dimensional fractional di erential equation with Dirichlet boundary condition.…”