Hardy-type inequalities in fractional h-discrete calculus

Abstract

The first power weighted version of Hardy’s inequality can be rewritten as where the constant is sharp. This inequality holds in the reversed direction when . In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus. Moreover, we prove that the corresponding constants are sharp.

Chebyshev type inequalities with fractional delta and nabla h-sum operators

“…And, the fractional order discrete Chebyshev type inequalities are studied in [3,11]. Also, there are the fractional analogues of some well-known inequlities in the literature, see [1,2,4,5,15,21]. For more knowledge and applications about discrete and continuous fractional calculus, see [8,19,22].…”