New inequalities via Caputo-Fabrizio integral operator with applications

Abstract

<abstract><p>Fractional integral inequalities have become one of the most useful and expansive tools for the development of many fields of pure and applied mathematics over the past few years. Many authors have just recently introduced various generalized inequalities that involved the fractional integral operators. The main goal of the present study is to incorporate the concept of strongly $ \left(s, m\right) $-convex functions and Hermite-Hadamard inequality with Caputo-Fabrizio integral operator. Also, we consider a new identity for twice differentiable mapping in the context of Caputo-Fabrizio fractional integral operator. Then, considering this identity as an auxiliary result, new mid-point version using well known inequalities like Hölder, power-mean, Young are presented. Moreover, some graphs of obtained inequalities are given for better understanding by the reader. Finally, we discussed some applications to matrix inequalities and spacial means.</p></abstract>