On Approximate Solution Of Fractional Order Logistic Equations By Operational Matrices Of Bernstein Polynomials

Abstract

In this Paper we give a scheme for the numerical solution of fractional order Logistic equations (FOLE) using operational matrices for fractional order integration and multiplications based on Bernstein Polynomials (BPs). By this method we get the FOLE in the form of a system of algebraic equations which is simple in handling for the numerical solutions and better approximations are obtained. For the illustration of the efficiency and simplicity of the scheme, three examples are added in the paper.

A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach

“…In this section, a kind of Jon von Neumann techinque is used to discuss the stability of Scheme (8).…”

“…In Chen et al presented a boundary‐type RBF collocation method for solving time fractional diffusion equations. Also, Khan et al presented the approximate solution with Bernstein polynomials for solving fractional order logistic equations. For more details, we refer to the recent advances in the fractional differential equations and variable order fractional optimal control problems .…”

On solving fractional logistic population models with applications

“…Among them, the Adams-type predictor-corrector method (El-Sayed et al 2007), the iterative method (Bhalekar and Daftardar-Gejji 2012), the optimal homotopy analysis method (Mohamed 2014), the weighted Mittag-Leffler functions method (West 2015), and the spectral iterative method (Shoja et al 2016). Khan et al (2015) considered the above model and used the operational matrices of Bernstein polynomials (OMBP) for getting its approximate solutions on t ∈ [0, 1] at three different choices of r , λ, and the absolute errors were about 10 −5 , see Figs. 2, 4, and 6 in Khan et al (2015).…”

An accurate method for solving a singular second-order fractional Emden-Fowler problem

“…Kumar et al [37] constituted a numerical algorithm based on the fractional homotopy analysis transform method to study the fractional model of Lienard's equations. Baleanu et al [38][39][40][41][42][43][44] considered the exact solutions of wave equations by the help of the local fractional Laplace variation iteration method (LFLVIM). They developed an iterative scheme for the exact solutions of local fractional wave equations (LFWEs).…”