A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

Advances in Difference Equations

article

Khan, Aziz¹  Alshehri, Hashim M.²  Gómez-Aguilar, J. F.³  Khan, Zareen A.⁴  Fernández-Anaya, G.⁵ 

[1] Department of Mathematics and General Sciences, Prince Sultan University;Mathematics Department, Faculty of Sciences;CONACyT-Tecnológico Nacional de México/CENIDET;College of Science, Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University;Departamento de Física y Matemáticas, Universidad Iberoamericana

关键词: Adams–Bashforth–Moulton scheme;    Predator–prey model;    Variable-order FO derivative;    Atangana–Baleanu FO derivative;    Mittag-Leffler kernel;   

DOI  :  10.1186/s13662-021-03340-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

【 授权许可】

CC BY