Properties of right fractional sum and right fractional difference operators and application

Abstract

In this paper, the concepts of a right fractional sum and right fractional difference operators are introduced. Some basic properties of a right fractional sum and right fractional difference operators are proved. According to these properties of a right fractional sum and right fractional difference operators, we studied an initial problem and a boundary value problem with two-point boundary conditions. We hope that the present work will facilitate solving a fractional difference equation with right fractional difference operators.

Symmetric duality for left and right Riemann–Liouville and Caputo fractional differences

“…More generally, it is also possible to investigate fractional calculus on an arbitrary time scale (that is, on an arbitrary nonempty closed set of the real numbers) [18][19][20][21]36]. The literature on the discrete fractional calculus is now vast: see [9,10,35,38,39] and references therein. For a comprehensive treatment, related topics of current interest and an extensive list of references, we refer the interested readers to the book [28].…”