Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 16, Issue -, Pages -Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/2021016
Keywords
Extended (G '/G)-expansion method; generalized (G '/G)-expansion method; fractional-order biological population models; traveling wave solutions; Riemann-Liouville's derivative; complex transformation
Categories
Funding
- CONACyT: Catedras CONACyT para jovenes investigadores
- SNI-CONACyT
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In this paper, generalized and extended methods were implemented to solve fractional-order biological population models, providing effective information through constructing different families of traveling waves solutions and investigating the different physical behavior of the problems.
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.
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