Maryam A. AL-Towailb
In this article, we study the regular -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, . 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
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