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On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator

Department SBAI, Università di Roma “La Sapienza”, 00161 Roma, Italy
Current address: Via Antonio Scarpa 16, 00161 Roma, Italy.
Axioms 2020, 9(2), 61; https://doi.org/10.3390/axioms9020061
Received: 30 March 2020 / Revised: 17 May 2020 / Accepted: 19 May 2020 / Published: 25 May 2020
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative in space. We approximate the solution by the Schoenberg-Bernstein operator, which is a spline positive operator having shape-preserving properties. The unknown coefficients of the approximating operator are determined by a collocation method whose collocation matrices can be constructed efficiently by explicit formulas. The numerical experiments we conducted show that the proposed method is efficient and accurate. View Full-Text
Keywords: fractional differential problem; Caputo fractional derivative; B-spline; quasi-interpolant operator; collocation method fractional differential problem; Caputo fractional derivative; B-spline; quasi-interpolant operator; collocation method
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MDPI and ACS Style

Pitolli, F. On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator. Axioms 2020, 9, 61. https://doi.org/10.3390/axioms9020061

AMA Style

Pitolli F. On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator. Axioms. 2020; 9(2):61. https://doi.org/10.3390/axioms9020061

Chicago/Turabian Style

Pitolli, Francesca. 2020. "On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator" Axioms 9, no. 2: 61. https://doi.org/10.3390/axioms9020061

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