A time‐fractional competition ecological model with cross‐diffusion. (10th February 2020)

• Record Type: Journal Article
• Authors: Manimaran, J.; Shangerganesh, L.; Debbouche, Amar
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 8(2020)
• Page Start: 5197
• Page End: 5211
• Publication Date: 2020-02-10
• Subjects: cross‐diffusion -- energy estimates -- Faedo‐Galerkin method -- fractional reaction‐diffusion equations -- Lotka‐Volterra competition system -- numerical and simulations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6260
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.