Travelling waves solution for fractional-order biological population model

Abstract

In this paper, we implemented the generalized (G′/G) and extended (G′/G) methods to solve fractional-order biological population models. The fractional-order derivatives are represented by the Caputo operator. The solutions of some illustrative examples are presented to show the validity of the proposed method. First, the transformation is used to reduce the given problem into ordinary differential equations. The ordinary differential equation is than solve by using modified (G′/G) method. Different families of traveling waves solutions are constructed to explain the different physical behavior of the targeted problems. Three important solutions, hyperbolic, rational and periodic, are investigated by using the proposed techniques. The obtained solutions within different classes have provided effective information about the targeted physical procedures. In conclusion, the present techniques are considered the best tools to analyze different families of solutions for any fractional-order problem.

Noise effect on soliton phenomena in fractional stochastic Kraenkel-Manna-Merle system arising in ferromagnetic materials

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Study of traveling soliton and fronts phenomena in fractional Kolmogorov-Petrovskii-Piskunov equation

“…These nonlinear FPDEs have a high potential for use in a variety of domains, prompting academics to devote substantial time and effort to discovering analytical and numerical solutions [8][9][10][11][12]. To discover precise answers, Numerous efficient and trustworthy methods, including the unified method [13], exp-function approach [14], residual power series method [15], Kudryashov method [16], replicating kernel method [17], and others, have been developed by researchers.These approaches include the first integral method [18], Laplace Adomian decomposition method [19,20], natural transform decomposition method [21,22], homotopy analysis method [23], (G'/G)-enpension method [24][25][26], modified simple equation method [27], and EDAM [28,29].…”

Exploring Propagating Soliton Solutions for the Fractional Kudryashov–Sinelshchikov Equation in a Mixture of Liquid–Gas Bubbles under the Consideration of Heat Transfer and Viscosity

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