Basic Properties of an Eigenparameter-Dependent $q$-Boundary Value Problem

F. Ayca Cetinkaya

This paper is devoted to study a $q$-fractional boundary value problem that includes $q$-Jackson derivative in the differential equation and an eigenvalue parameter in the boundary condition. We introduced a modified Hilbert space and a symmetric operator. We illustrated the examined boundary value problem as a spectral problem for this operator. Properties of the eigenvalues and eigenfunctions are investigated and the Green's function is constructed.