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Article

A Collocation Method Based on Discrete Spline Quasi-Interpolatory Operators for the Solution of Time Fractional Differential Equations

by 1,†, 2,‡ and 2,*,‡
1
Department IIIE, University of L’Aquila, 67100 L’Aquila, Italy
2
Department SBAI, University of Roma “La Sapienza”, 00161 Roma, Italy
*
Author to whom correspondence should be addressed.
Current address: Department IIIE, University of L’Aquila, Piazzale Ernesto Pontieri 2, Monteluco di Roio, 67100 L’Aquila, Italy.
Current address: Department SBAI, University of Roma “La Sapienza”, Via Antonio Scarpa 16, 00161 Roma, Italy.
Received: 28 November 2020 / Revised: 30 December 2020 / Accepted: 31 December 2020 / Published: 5 January 2021
In many applications, real phenomena are modeled by differential problems having a time fractional derivative that depends on the history of the unknown function. For the numerical solution of time fractional differential equations, we propose a new method that combines spline quasi-interpolatory operators and collocation methods. We show that the method is convergent and reproduces polynomials of suitable degree. The numerical tests demonstrate the validity and applicability of the proposed method when used to solve linear time fractional differential equations. View Full-Text
Keywords: fractional differential equation; quasi-interpolatory operator; collocation method; B-spline fractional differential equation; quasi-interpolatory operator; collocation method; B-spline
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MDPI and ACS Style

Pellegrino, E.; Pezza, L.; Pitolli, F. A Collocation Method Based on Discrete Spline Quasi-Interpolatory Operators for the Solution of Time Fractional Differential Equations. Fractal Fract. 2021, 5, 5. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010005

AMA Style

Pellegrino E, Pezza L, Pitolli F. A Collocation Method Based on Discrete Spline Quasi-Interpolatory Operators for the Solution of Time Fractional Differential Equations. Fractal and Fractional. 2021; 5(1):5. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010005

Chicago/Turabian Style

Pellegrino, Enza, Laura Pezza, and Francesca Pitolli. 2021. "A Collocation Method Based on Discrete Spline Quasi-Interpolatory Operators for the Solution of Time Fractional Differential Equations" Fractal and Fractional 5, no. 1: 5. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010005

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