Nabla Discrete fractional Calculus and Nabla Inequalities

TL;DR

This paper introduces a new Caputo-like discrete nabla fractional difference, develops fractional Taylor formulas, and derives related inequalities, advancing the mathematical framework of discrete fractional calculus.

Contribution

It is the first to define a Caputo-like discrete nabla fractional difference, formulate fractional Taylor formulas, and establish associated inequalities.

Findings

Defined a Caputo-like discrete nabla fractional difference

Developed discrete nabla fractional Taylor formulas

Derived nabla fractional Opial, Ostrowski, Poincare, and Sobolev inequalities

Abstract

Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincare and Sobolev type inequalities.