Some generalizations of dynamic Opial-type inequalities in conformable calculus

Abstract

Abstract In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α = 1 $\alpha = 1$ , our results cover some well-known inequalities of Opial-type on time scales.

Keywords

• Opial-type inequality
• Dynamic inequality
• Hölder inequality
• Conformable fractional calculus