Existence of solution for a fractional-order Lotka-Volterra reaction-diffusion model with Mittag-Leffler kernel. (English) Zbl 1459.35378
Summary: 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35K45 | Initial value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 92D25 | Population dynamics (general) |
Keywords:
ABC fractional derivative; existence and uniqueness of solution; HU stability; Lotka-Volterra diffusion modelReferences:
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