A new generalization of the Katugampola generalized fractional integrals in terms Mittag-Leffler functions is proposed. Consequently, generalizations Hermite-Hadamard inequalities by this newly proposed integral operator, for a positive convex stochastic process, are established. Other known results easily deduced as particular cases these inequalities. The obtained also hold any function.

In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method discussion is to study solutions equivalent Volterra integral equation in terms Mittag–Leffler functions. existence and uniqueness results are established by using Schauder's fixed point theorem Banach's theorem, respectively. An example given illustrate main results.

This paper aims to study the bounds of k-integral operators with Mittag-Leffler kernel in a unified form. To achieve these bounds, definition exponentially (α,h−m)−p-convexity is utilized frequently. In addition, fractional Hadamard type inequality which shows upper and lower simultaneously presented. The results are directly linked many published articles.

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 order to be able study cosmic phenomena more accurately and broadly, it was necessary expand the concept of calculus. this study, we aim introduce a new fractional Hermite–Hadamard–Mercer’s inequality its integral type inequalities. To facilitate that, use proportional operators integrable functions with respect another continuous strictly increasing function. Moreover, establish some weight...

Integral inequalities for ?-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented via operator. A novel parameterized auxiliary identity involving proposed differentiable mappings. By identity, we derive several Ostrowski whose absolute values It that the obtained outcomes exhibit classical c...