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A time‐fractional competition ecological model with cross‐diffusion
Author(s) -
Manimaran J.,
Shangerganesh L.,
Debbouche Amar
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6260
Subject(s) - mathematics , convergence (economics) , competition (biology) , diffusion , galerkin method , fractional calculus , competition model , reaction–diffusion system , order (exchange) , discontinuous galerkin method , mathematical optimization , finite element method , mathematical analysis , ecology , physics , profit (economics) , finance , economics , biology , microeconomics , economic growth , thermodynamics
This paper is concerned with some mathematical and numerical aspects of a Lotka‐Volterra competition time‐fractional reaction‐diffusion system with cross‐diffusion effects. First, we study the existence of weak solutions of the model following the well‐known Faedo‐Galerkin approximation method and convergence arguments. We demonstrate the convergence of approximate solutions to actual solutions using the energy estimates. Next, the Galerkin finite element scheme is proposed for the considered model. Further, various numerical simulations are performed to show that the fractional‐order derivative plays a significant role on the morphological changes of the considered competition model.