Investigating biological population model using exp-function method

Abstract

This paper is the spectator of the arrangement of an efficient transformation and exp-function technique to build up generalized exact solutions of the biological population model equation. Computational work and subsequent numerical results re-identify the effectiveness of proposed algorithm. It is pragmatic that recommended plan is greatly consistent and may be comprehensive to other nonlinear differential equations of fractional order.

Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation

“…Applying J to both sides of Equation (42), then Equations (42) and (43) are equivalent to the integral equation…”

“…[20][21][22][23][24][25][26][27][28] Solving partial differential equations with fractional derivatives is often more difficult than solving the classical type, for its operator is defined by integral. In the recent year, researchers have developed some iterative methods for solving the nonlinear fractional differential equations, such as Adomian decomposition method, 21,28,29 variational iteration method, [30][31][32] homotopy decomposition method, 33 differential transform method, 34,35 permuturbation iteration transformation method, 36 homotopy-perturbation method, 28,37 homotopy analysis method, [38][39][40] exp-function method, [41][42][43] wavelet method, 44 Khater method, 45 and residual power series method. 46,47 In this paper, we consider the time-fractional Cahn-Hilliard (TFCH) equations of the fourth and sixth order given, respectively, as follows:…”

Investigation of dephasing in an open quantum system under chaotic influence via a fractional Kohn–Sham scheme

“…The fractional derivative used here is the modified RL operator developed in Jumarie . This operator has proven to have been very useful and simple to be implemented for modeling nonlinear and complex phenomena . As can be seen in eq.…”

Solving Nonlinear Evolution Equations by <i>(G'/G)</i>-Expansion Method

“…In this technique, a linear ordinary differential equation of second order is used, as the auxiliary equation. (G´/G)-expansion method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] applied to solve the various types of the nonlinear evolution equations. A new modification introduced by Zhao et al [17] in (G´/G)-expansion method.…”