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A study of fractional Lotka‐Volterra population model using Haar wavelet and Adams‐Bashforth‐Moulton methods
Author(s) -
Kumar Sunil,
Kumar Ranbir,
Agarwal Ravi P.,
Samet Bessem
Publication year - 2020
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.6297
Subject(s) - mathematics , haar wavelet , wavelet , algebraic number , mathematical optimization , discrete wavelet transform , mathematical analysis , wavelet transform , computer science , artificial intelligence
The Lotka‐Volterra (LV) system is an interesting mathematical model because of its significant and wide applications in biological sciences and ecology. A fractional LV model in the Caputo sense is investigated in this paper. Namely, we provide a comparative study of the considered model using Haar wavelet and Adams‐Bashforth‐Moulton methods. For the first method, the Haar wavelet operational matrix of the fractional order integration is derived and used to solve the fractional LV model. The main characteristic of the operational method is to convert the considered model into an algebraic equation which is easy to solve. To demonstrate the efficiency and accuracy of the proposed methods, some numerical tests are provided.