Geodesic
Basic Properties of an Eigenparameter-Dependent $q$-Boundary Value Problem
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 4, p. 503 .

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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.
Classification : 34B08 34L05
Keywords: $q$-Jackson derivative, Sturm-Liouville operator, eigenvalues and eigenfunctions 
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     author = {F. Ayca Cetinkaya},
     title = {Basic {Properties} of an {Eigenparameter-Dependent} $q${-Boundary} {Value} {Problem}},
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F. Ayca Cetinkaya. Basic Properties of an Eigenparameter-Dependent $q$-Boundary Value Problem. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 4, p. 503 . http://geodesic.mathdoc.fr/item/KJM_2019_43_4_a0/