A study of fractional Lotka‐Volterra population model using Haar wavelet and Adams‐Bashforth‐Moulton methods. (19th February 2020)

• Record Type: Journal Article
• Authors: Kumar, Sunil; Kumar, Ranbir; Agarwal, Ravi P.; Samet, Bessem
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 8(2020)
• Page Start: 5564
• Page End: 5578
• Publication Date: 2020-02-19
• Subjects: Adams‐Bashforth‐Moulton method -- fractional LV model -- Haar wavelet method -- operational matrix; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6297
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.