A unified approach for novel estimates of inequalities via discrete fractional calculus techniques

Abstract

In this article, we introduce the discrete fractional sum equations and inequalities. Some new generalized Grüss type discrete fractional sum inequalities are developed. We employ a nabla or backward difference; we employ the Riemann-Liouville definition of the fractional difference. Furthermore, the current research is a discrete variant of fundamental inequalities set up in the recent literary works and extends a few discrete version for ∇-fractional sum specifically on time scale ℏN, where 0<ℏ⩽1.

Keywords

• 39A12
• 26A33
• 26D15