Incorporating fractional operators into interaction dynamics studies: An eco-epidemiological model

Analytical solutions are the most effective tools for understanding phenomena modeled with differential equations. On the other hand, analytical solvers may be limited in their ability to handle complex problems and we are forced to rely on approximate and numerical methods. Through the investigation of two types of fractional operators, this article aims to investigate both approaches to studying the interactive dynamics of an eco-epidemiological diffusion model. We consider two differential operators in our main model: local beta time and non-local Riesz space fractional derivative. Firstly, we propose novel classes of soliton wave solutions for the local time fractional version of the system using two efficient analytical methods. In the second part of the paper, we consider the case where the second-order space derivative operator in the problem is of the type of Riesz fractional operator that is non-local. A finite difference scheme is the main idea behind discretizing this fractional system. Throughout this article, we highlight the validity and efficiency of both analytical and numerical perspectives. The results can be examined by epidemiologists for a more comprehensive interpretation.