Opial Inequalities on Timescales Via Fractional Conformable Calculus

Abstract

In this work, we prove a new class of weighted inequalities of Opial type via conformable fractional calculus on timescales. The inequalities obtained unify and generalize a number of results previously established in the literature, while also provide significant improvements. Furthermore, we apply our findings to determine the distance between successive zeros of solutions to conformable fractional dynamic equations with damping terms. In addition, we obtain lower bounds for the distance between a zero of a solution and a zero of its derivative in the conformable fractional sense. our results provide suitable conditions for the right and left disfocality, as well as the disconjugacy, of such conformable fractional dynamic equations on compact intervals timescales.