Some generalizations of dynamic Opial-type inequalities in conformable calculus

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2024年11月29日

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Fatma M. Khamis,
M. M. A. El-Sheikh,
Thabet Abdeljawad,
Aiman Mukheimer,
Gamal A. F. Ismail

摘要

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.