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An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

1
Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India
2
Institute of Industry Revolution 4.0, National University of Malaysia, UKM Bangi 43600, Selangor, Malaysia
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Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
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Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
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Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4, 06790 Etimesgut, Turkey
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01069 Dresden, Germany
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 558; https://doi.org/10.3390/math8040558
Received: 14 March 2020 / Revised: 5 April 2020 / Accepted: 7 April 2020 / Published: 10 April 2020
(This article belongs to the Special Issue Qualitative Theory of Fractional-Order Systems)
In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams–Bashforth–Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams–Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method. View Full-Text
Keywords: Bernstein wavelets; operational matrix; fractional differential equations; Adams–Bashforth–Moulton predictor correcter scheme Bernstein wavelets; operational matrix; fractional differential equations; Adams–Bashforth–Moulton predictor correcter scheme
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MDPI and ACS Style

Kumar, S.; Ahmadian, A.; Kumar, R.; Kumar, D.; Singh, J.; Baleanu, D.; Salimi, M. An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets. Mathematics 2020, 8, 558.

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