On φ−Convex Stochastic Processes and Integral Inequalities Related

In this paper the concept of φ−convex stochastic process is introduced and certain algebraic properties are deduced. Also, some mean square integral inequalities of Hermite-Hadamard type are established. In addition, various mean square integral inequalities are investigated to find upper estimates using of the weighted arithmetic mean, the weighted power mean of order p and the logarithmic mean

On Generalized Harmonically ψ-MT-Convex Functions via Local Fractional Integrals and some Applications

In this work, we introduce a new class of harmonically convex functions, namely, generalized harmonically ψ-MT-convex functions established on fractal set techniques, for establishing inequalities of Hermite-Hadamard type and certain related variants with respect to the Raina’s function. With the help of an auxiliary identity associated with Raina’s function, by generalized Holder inequality and generalized power mean, generalized midpoint type, Ostrowski type, and trapezoid type inequalities via local fractional integral for generalized harmonically ψ-MT-convex functions are given. The introduced technique gives the results by establishing some special values for the parameters or applying restrictive suppositions and is entirely practicable for regaining the existing inequalities in the related literature

On Non Conformable Fractional Laplace Transform

In the present paper, the main theorems of the classical Laplace transform are generalized in the non-conforming Laplace transform with nucleus et−α . We calculate the Laplace transform of non-conforming agreement of this kernel from some elementary functions and establish the non-conforming version of the transform of the successive derivative, the integral of a function and the convolution of fractional functions. In addition, the bounded and the existence of the non-conforming Laplace transform is presented. Finally, we show the application of N1− Transform to solving fractional differential equations

Concerning the Inequality of Hermite-Hadamard Generalized

n this paper, we present new extensions of the Hermite-Hadamard type generalized inequalities for convex functions, within the framework of a generalized operator integral. Results are general in nature