Conformable fractional Dirac system on time scales

Abstract

We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale . Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on . So, we provide a constructive procedure for the solution of this problem. These results are important steps to consolidate the link between fractional calculus and time scale calculus in spectral theory.

Parameter-Dependent Dirac Systems on Time Scales

“…Although, the literature about the spectral problems for Sturm-Liouville equation on time scales is vast; there are only a few studies about Dirac-type dynamic equation systems. It can be referred [21] and [22] for example to boundary-value problems generated by the Dirac system on a time scale.…”

Spectral Properties of a Conformable Boundary Value Problem on Time Scales

“…Recently, researchers have started to deal with studies relating to conformable calculus on time scales (see [10][11][12][13][14][15][16]).…”

A new definition of conformable fractional derivative on arbitrary time scales

“…In both definitions, it is obvious that T 0 (f ) = f , and it is not conformable according to Definition 1.2. There are several follow-up papers using at least one of the above conformable definitions, including [3][4][5][6][7][8][9]. The authors in [1] have also mentioned the possible extension of conformation derivatives on time scales (see [1], Remark 1.5) via…”