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

Date

2017-03-28

Authors

AL-Towailb, Maryam A.

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

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, α ∈ (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.

Description

Keywords

Boundary value problems, Eigenvalues and eigenfunctions, Left and right sided Riemann-Liouville, Caputo q-fractional derivatives

Citation

AL-Towailb, M. A. (2017). A q-fractional approach to the regular Sturm-Liouville problems. <i>Electronic Journal of Differential Equations, 2017</i>(88), pp. 1-13.

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Attribution 4.0 International

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