Electron. J. Differential Equations, Vol. 2017 (2017), No. 88, pp. 1-13.

A q-fractional approach to the regular Sturm-Liouville problems

Maryam A. AL-Towailb

In this article, we study the regular $q$-fractional Sturm-Liouville problems that include the right-sided Caputo q-fractional derivative and the left-sided Riemann-Liouville q-fractional derivative of the same order, $\alpha \in (0,1)$. We prove properties of the eigenvalues and the eigenfunctions in a certain Hilbert space. We use a fixed point theorem for proving the existence and uniqueness of the eigenfunctions. We also present an example involving little q-Legendre polynomials.

Submitted January 27, 2017. Published March 28, 2017.
Math Subject Classifications: 39A13, 26A33, 34L10.
Key Words: Boundary value problems; eigenvalues and eigenfunctions; left and right sided Riemann-Liouville and Caputo q-fractional derivatives.

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Maryam A. AL-Towailb
Department of Natural and Engineering Sciences
Faculty of Applied Studies and Community Service
King Saud University, Riyadh, SA
email: mtowaileb@ksu.edu.sa

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