On innovations of the multivariable fractional Hardy-type inequalities on time scales

Abstract

Fractional integral-type inequalities, dynamic equations, integral operators and variable expo-nents have an important place in time scales theory and harmonic analysis. Our main goal in this study is to obtain the multivariable fractional Hardy-type integral inequality using a new version of Jensen's inequality for super-quadratic and sub-quadratic functions on time scales with variable exponents.