Abstract
In this article, a new type of fractional sums and differences called the discrete weighted fractionaloperators are presented. The weighted backward and forward difference operators are defined on anisolated time scale with arbitrary step size and they obey the power law.
Highlights
The continuous fractional calculus is a rich field of research and it has attracted the attention of several researchers working in diverse fields of science, engineering, economics and medicine [1, 2]
We have proposed the left and right weighted fractional sums and differences with a study of the action of the Q-operator
In the right case Q-versions of weighted fractional sums and differences and some conditions on the weight ω(t) have been given to have coincidence with those verifying the integration by parts rule
Summary
The continuous fractional calculus is a rich field of research and it has attracted the attention of several researchers working in diverse fields of science, engineering, economics and medicine [1, 2]. J Frac Calc & Nonlinear Sys inside and outside the integral operator used in the definition They studied many basic properties that are essential for researchers to apply theoretically and use in their modelling problems.
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