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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.

Towards a non-conformable fractional calculus of n-variables

Martínez Francisco, Nápoles Juan E. Valdés

Journal of Mathematics and Applications

2020

Vol. 43

87--98

In this paper we present an extension of the non-conformable local fractional derivative, to the case of functions of several variables. Results analogous to those known from the classic multivariate calculus are presented. To show the strength of this approach, we show an extension of the Second Lyapunov Method to the non-conformable local fractional case.