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Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel
Author(s) -
Khan Hasib,
Li Yongjin,
Khan Aftab,
Khan Aziz
Publication year - 2019
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.5590
Subject(s) - mathematics , uniqueness , fractional calculus , kernel (algebra) , order (exchange) , stability (learning theory) , volterra equations , reaction–diffusion system , mittag leffler function , diffusion , mathematical analysis , pure mathematics , nonlinear system , thermodynamics , computer science , physics , finance , quantum mechanics , machine learning , economics
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.