Several fractional integral inequalities of the Hermite–Hadamard type are presented for class (h,g;m)-convex functions. Applied operators contain extended generalized Mittag-Leffler functions as their kernel, thus enabling new that extend and generalize known results. As an application, upper bounds given.

The theory of fractional analysis has been a focal point fascination for scientists in mathematical science, given its essential definitions, properties, and applications handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest calculus convexity due to wide range almost all branches applied sciences, especially numerical analysis, physics...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

In this paper, the authors defined a new general class of functions, so-called strongly (h1,h2)-nonconvex function involving F??,?(?) (Raina function). Utilizing this, some Hermite-Hadamard type integral inequalities via generalized fractional operator are obtained. Some results as special cases given well.

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are generalization of some results that existed in the literature.

In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations...