Fractional singular Sturm-Liouville problems on the half-line

Advances in Difference Equations

Pisamai Kittipoom¹ 

[1] Applied Analysis Research Unit, Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University;

关键词: fractional Sturm-Liouville problem;    Riemann-Liouville derivative;    Caputo derivative;    Weyl fractional derivative;    fractional Laguerre equation;    space-fractional diffusion equation;   

DOI  :  10.1186/s13662-017-1370-4

来源: DOAJ

【 摘 要 】

Abstract In this paper, we consider two types of singular fractional Sturm-Liouville operators. One comprises the composition of left-sided Caputo and left-sided Riemann-Liouville derivatives of order α ∈ ( 0 , 1 ) $\alpha \in(0,1)$ . The other one is the composition of left-sided Riemann-Liouville and right-sided Caputo derivatives. The reality of the corresponding eigenvalues and the orthogonality of the eigenfunctions are proved. Furthermore, we formulate the fractional Laguerre Strum-Liouville problems and derive the explicit eigenfunctions as the non-polynomial functions related to Laguerre polynomials. Finally, we introduce the generalized Laguerre transform and employ it to solve the unbounded space-fractional diffusion equations.

【 授权许可】

Unknown