Dynamical study of fractional order mutualism parasitism food web module

By Aziz Khan, Thabet Abdeljawad, José Francisco Gómez‐Aguilar, Hasib Khan. 2020

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Abstract In literature, many researchers have examined food web modules for different aspects and kinds such as exploitative competition, energy flow web, apparent competition, source web, trophic cascades of food chains, functional web, paleoecological web and intraguild predation. These food webs have been analyzed for competition and predation, where as the module connected with mutualism and parasitism have attracted the attention of researchers. In this article, we study mutualism parasitism food web module (MPFWM) by replacing the ordinary derivative by Atangana-Baleanu (AB) fractional order (FO) derivative, which is a generalization of classical derivative. This new type of operators enables us to use the essential information of the variables in the nonlocal systems. Existence and uniqueness (EU) of solutions have been proved by employing fixed point theorem. Picard’s stability approach is used for the stability analysis. Finally, numerical solutions of the ABC fractional order MPFWM were obtained for the particular parameter values.

Subfields: Modeling and Simulation, Plant Science, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/163c6ab1aa010964d8d7983f7f51b55250c7cc5e