4 papers
Self-similar solutions to the time-fractional Porous-Medium Equation
David Gómez-Castro, Åukasz PÅociniczak, Juan Luis Vázquez
We show the existence of self-similar solutions with constant finite mass to the time-fractional Porous-Medium Equation for all spatial dimensions and all exponents $m>m_…
Fractional Derivatives: an extension of classical analysis to non-integer orders
Félix del Teso, David Gómez-Castro
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both…
Finite Elements with weighted bases for the fractional Laplacian
Félix del Teso, Stefano Fronzoni, David Gómez-Castro
This work presents a numerical study of the Dirichlet problem for the fractional Laplacian with using Finite Element methods with non-standard bases. Classica…
Convergence of a finite-volume scheme for aggregation-diffusion equations with saturation
David Gómez-Castro
In [Bailo, Carrillo, Hu. SIAM J. Appl. Math. 2023] the authors introduce a finite-volume method for aggregation-diffusion equations with non-linear mobility. In this paper we prove…