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Fractal Fract 2018, 2(1), 13; https://doi.org/10.3390/fractalfract2010013

A Fractional B-spline Collocation Method for the Numerical Solution of Fractional Predator-Prey Models

Department of Basic and Applied Sciences for Engineering (SBAI), University of Roma “La Sapienza”, Via Antonio Scarpa 16, 00161 Roma, Italy
Received: 22 December 2017 / Revised: 12 February 2018 / Accepted: 12 February 2018 / Published: 17 February 2018
(This article belongs to the Special Issue Fractional Dynamics)
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Abstract

We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost. View Full-Text
Keywords: nonlinear fractional differential system; fractional predator-prey model; fractional B-spline; collocation method nonlinear fractional differential system; fractional predator-prey model; fractional B-spline; collocation method
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Pitolli, F. A Fractional B-spline Collocation Method for the Numerical Solution of Fractional Predator-Prey Models. Fractal Fract 2018, 2, 13.

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