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On Opial-type inequality for a generalized fractional integral operator

Vivas-Cortez Miguel, Martínez Francisco, Valdes Juan E. Nápoles, Hernández Jorge E.

Demonstratio Mathematica

2022

Vol. 55, nr 1

695--709

This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the parameters involved, the established results in the work are obtained. In addition, some criteria are established to obtain the aforementioned inequalities based on other integral operators. Finally, a more generalized definition is suggested, with which interesting results can be obtained in the field of fractional integral inequalities.

Opial-type inequalities for conformable fractional integrals

Sarikaya Mehmet Zeki, Budak Hüseyin

Journal of Applied Analysis

2019

Vol. 25, nr 2

155--163

In this paper, we establish the Opial-type inequalities for a conformable fractional integral and give some results in special cases of α. The results presented here would provide generalizations of those given in earlier works.

Some new generalizations of Maroni inequality on time scales

Yin L., Zhao C.

Demonstratio Mathematica

2013

Vol. 46, nr 4

645--654

The aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.

Integral inequalities associated with inequalities of Opial type

Florkiewicz B., Kuchta M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 1

41-45

We derive some new integral inequalities of the form: [...], h [belongs to] H, where I = (alpha, beta), -[infinity is less than or equal alpha < beta is less than or equal infinity], p > 0, H is a wide class of absolutely continuous functions h defined on I and satisfying the limit conditions h(alpha) = 0 or h(beta) = 0, the functions r, s and u are any set of functions related by the appropriate weight functions. To get the desired inequality, at first we derive an integral inequality of Opial type using a uniform method of obtaining integral inequalities with weight functions involving the function and its derivative [2].