On a New Generalized Integral Operator and Certain Operating Properties

Paulo Guzman,Miguel Vivas-Cortez,Juan Nápoles Valdés,Luciano Lugo

doi:10.3390/axioms9020069

Paulo Guzman, Miguel Vivas-Cortez + Show 2 more

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https://doi.org/10.3390/axioms9020069

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Abstract

In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals.

Highlights

In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals
A fairly complete classification of these fractional operators is presented, with abundant information, on the other hand, in the work [3] some reasons are presented why new operators linked to applications and developments theorists appear every day
These operators had been developed by numerous mathematicians with a barely specific formulation, for instance, the Riemann–Liouville (RL), the Weyl, Erdelyi–Kober, Hadamard integrals and the Liouville and Katugampola fractional operators and many authors have introduced new fractional operators generated from general classical local derivatives

Summary

Preliminars

Integral Calculus is a mathematical area with so many ramifications and applications, that the sole intention of enumerating them makes the task practically impossible. The principle used to find models for fractional derivatives has been to define, first, a fractional integral Applicability in areas such as physics, engineering, biology, has managed to establish its usefulness and many important results have appeared in the literature. A fairly complete classification of these fractional operators is presented, with abundant information, on the other hand, in the work [3] some reasons are presented why new operators linked to applications and developments theorists appear every day These operators had been developed by numerous mathematicians with a barely specific formulation, for instance, the Riemann–Liouville (RL), the Weyl, Erdelyi–Kober, Hadamard integrals and the Liouville and Katugampola fractional operators and many authors have introduced new fractional operators generated from general classical local derivatives. In our work we are interested in presenting a generalization of these integral operators and applying to different known inequalities

A New Fractional Integral Operator

Extensions