Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions

• Main Authors: Mostafa M. A. Khater, Raghda A. M. Attia, Dianchen Lu
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Mathematical and Computational Applications
• Subjects: modified auxiliary equation method; conformable fractional derivatives; fractional biological population model; fractional equal with model; fractional modified equal width equation
• Online Access: https://www.mdpi.com/2297-8747/24/1/1

In this article, we present a modified auxiliary equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive <i>x</i>-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original equations via computer software such as Maple, Mathematica, and Matlab.