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An augmented-RBF method for solving fractional Sturm-Liouville eigenvalue problems

Antunes, Pedro R. S.; Rui A. C. Ferreira

SIAM Journal of Scientific Computing, 37(1) (2015), A515-A535

In this work we construct numerical schemes, using radial basis functions (RBFs), to solve Sturm--Liouville eigenvalue problems in which the so-called fractional derivatives are involved. We take into account the fact that the solutions to such problems might be nonsmooth and, consequently, we augment the space generated by RBF base functions with some fractional polynomials to overcome this problem. We show through some examples the effectiveness of our method.