4,784 research outputs found
Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.P.A. is partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific projects PEstOE/MAT/UI0208/2013 and PTDC/MAT-CAL/4334/2014. R.F. was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.info:eu-repo/semantics/publishedVersio
A Finite Element Method for the Fractional Sturm-Liouville Problem
In this work, we propose an efficient finite element method for solving
fractional Sturm-Liouville problems involving either the Caputo or
Riemann-Liouville derivative of order on the unit interval
. It is based on novel variational formulations of the eigenvalue
problem. Error estimates are provided for the finite element approximations of
the eigenvalues. Numerical results are presented to illustrate the efficiency
and accuracy of the method. The results indicate that the method can achieve a
second-order convergence for both fractional derivatives, and can provide
accurate approximations to multiple eigenvalues simultaneously.Comment: 30 pages, 7 figure
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