Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel. (21st March 2019)

• Record Type: Journal Article
• Authors: Khan, Hasib; Li, Yongjin; Khan, Aftab; Khan, Aziz
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 9(2019)
• Page Start: 3377
• Page End: 3387
• Publication Date: 2019-03-21
• Subjects: ABC fractional derivative -- existence and uniqueness of solution -- HU stability -- Lotka‐Volterra diffusion model; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5590
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In the literature, many researchers have studied Lotka‐Volterra (L‐V) models for different types of studies. In order to continue the study, we consider a fractional‐order L‐V model involving three different species in the Atangana‐Baleanu‐Caputo (ABC) sense of fractional derivative. This new model has potentials for a large number of research‐oriented studies. The first point that arises is whether the new model has a solution or not. Therefore, to answer this question, we consider the existence and uniqueness (EU) of the solutions and then Hyers‐Ulam (HU) stability for the proposed L‐V model.