Abstract
This work addresses the analytical investigation of the prey–predator behavior modeled by nonlinear evolution equation systems with fractional derivative order. Through the New Extended Algebraic Method (NEAM), we unearthed diverse types of soliton solutions including bright, dark solitons, combined trigonometric function solutions, and singular solutions. Besides the results obtained in the work of Khater, some new complex soliton solutions are also unearthed. The NEAM can also be used like the synthesis of the two mathematical tools.
Highlights
The coexistence and interfering of biological species have been one of the major concerns in wildlife reserves since the dawn of time
The implementation of mathematical models describing the behavior of these phenomena is a major asset in bio-mathematics, but the resolution of these systems remains a major concern
We are interested to the prey–predator mathematics model having a fractional derivative order as follows: Hαt scitation.org/journal/adv and β, δ, κ, and m are positive parameters
Summary
The coexistence and interfering of biological species have been one of the major concerns in wildlife reserves since the dawn of time. In this particular work, we are interested to the prey–predator mathematics model having a fractional derivative order as follows: Hαt. Thereafter, we apply the NEAM to investigate diverse soliton solutions to the mathematical model of the fractional derivative order of the PP system. (ii) Substituting Eq (10) or Eq (11) into Eq (7), the obtained soliton solutions to the prey population size give. The analytical survey soliton solutions of the prey population are given by the following:. (i) Plug Eq (32) or Eq (33) into Eq (7), we set out the soliton solutions to the prey population size, H3,1(ξ). (ii) Using Eq (34) or Eq (35), we set out the soliton solutions to the prey population size, H3,6. The generalized hyperbolic and triangular function are given in Refs. 21 and 22
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