Conformable fractional Sturm–Liouville problems on time scales

Abstract

We consider a conformable fractional Sturm-Liouville problem on bounded time scales. Firstly, the existence and uniqueness of solutions of the conformable fractional Sturm-Liouville problem are proved. Maximal and minimal symmetric operators are introduced and some results are given. Finally, the Green's function of this problem is constructed, and an eigenfunction expansion is given.

Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions

“…Fractional eigenvalue problems have also been considered within the framework of tempered fractional calculus [ 12 , 13 ] and conformable fractional calculus [ 14 , 15 , 16 , 17 ]. Recently, a fractional Sturm–Liouville operator containing composite fractional derivatives has been proposed in paper [ 18 ], and Prabhakar derivatives were applied in the construction of fractional eigenvalue problems subjected to homogeneous Dirichlet or mixed boundary conditions in papers [ 19 , 20 ].…”

Eigenvalue problems for a class of Sturm-Liouville operators on two different time scales

“…Spectral properties the classical Sturm-Liouville problem on time scales were given in various publications (see e.g. [1], [2], [5]- [9], [11], [17]- [25], [27]- [30], [34]- [37], [39] and references therein). However, there is no any publication about the Sturm-Liouville equation with a frozen argument on an arbitrary time scale.…”

Impulsive Sturm-Liouville Problems on Time Scales

“…This theory aims to unify continuous-time and discrete-time equations. Due to its numerous application in science, many authors have obtained a lot of results about this subject (see [4,7,5,6,10,11,13,20]).…”