Maryam A. AL-Towailb
Abstract:
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 email: mtowaileb@ksu.edu.sa |
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