Abstract
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.
Highlights
The construction of mathematical models for real-world phenomena and development of efficacious techniques to define them is one of the most critical issues in applied mathematics biology, engineering, physics and other fields of science
Boonrod and Razzaghi discussed a numerical approach based on Legendre wavelets for examining fractional differential equations (FDEs) by the exact formula for Riemann–Liouville (RL) [22]
Numerical results and discussions for the fractional SIR epidemic model are completely discussed in Section 7 which is main part of the proposed work
Summary
The construction of mathematical models for real-world phenomena and development of efficacious techniques to define them is one of the most critical issues in applied mathematics biology, engineering, physics and other fields of science. There are several research articles on Bernstein polynomial for solving fractional differential equations [9,10,11]. Boonrod and Razzaghi discussed a numerical approach based on Legendre wavelets for examining fractional differential equations (FDEs) by the exact formula for Riemann–Liouville (RL) [22]. Several other analytical and numerical schemes have been used to examine fractional order models [24,25,26]. Numerical results and discussions for the fractional SIR epidemic model are completely discussed in Section 7 which is main part of the proposed work
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