On Opial-type inequality for a generalized fractional integral operator

Abstract

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.

Khalil Conformable fractional derivative and its applications to population growth and body cooling models

“…Among these are the conformable fractional derivative of Khalil [8] and Atangana [2]. Several investigations have been carried out by other authors in this direction [16]. Other investigations have directed their goals towards fractional derivatives with kernels involving special functions [5,6,17,18].…”