On nabla conformable fractional Hardy-type inequalities on arbitrary time scales

Abstract

Abstract The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.

Keywords

• Fractional calculus
• Calculus on time scales
• Conformable nabla derivative
• Conformable nabla integral
• Hardy’s inequality