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

Abstract

Fractional integral-type inequalities, dynamic equations, integral operators and variable exponents 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.