Fractional differential equations have become central tools for the accurate modeling of real-world phenomena in various fields. This work focuses on the discretization of the space-time fractional diffusion problem with Caputo derivative in time and Riesz-Caputo derivative in space. We introduce a collocation method based on a B-spline representation of the solution. This approach strategically exploits the symmetry properties of both the spline basis functions and the Riesz-Caputo operator, resulting in an efficient method for solving the given fractional differential problem. Preliminary numerical tests are presented to validate the proposed collocation method.
Numerical approximation of the space-time fractional diffusion problem / Pellegrino, E.; Pitolli, F.; Sorgentone, C.. - In: IFAC PAPERSONLINE. - ISSN 2405-8971. - 58:12(2024), pp. 390-394. (Intervento presentato al convegno 12th IFAC Conference on Fractional Differentiation and its Applications, ICFDA 2024 tenutosi a Bordeaux, France) [10.1016/j.ifacol.2024.08.222].
Numerical approximation of the space-time fractional diffusion problem
Pitolli F.;Sorgentone C.
2024
Abstract
Fractional differential equations have become central tools for the accurate modeling of real-world phenomena in various fields. This work focuses on the discretization of the space-time fractional diffusion problem with Caputo derivative in time and Riesz-Caputo derivative in space. We introduce a collocation method based on a B-spline representation of the solution. This approach strategically exploits the symmetry properties of both the spline basis functions and the Riesz-Caputo operator, resulting in an efficient method for solving the given fractional differential problem. Preliminary numerical tests are presented to validate the proposed collocation method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.