A q-FRACTIONAL APPROACH TO THE REGULAR STURM-LIOUVILLE PROBLEMS

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 Riema nn-Liouville q-fractional derivative of the same order, alpha epsilon (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.