The aim of this paper is to establish some integral inequalities for convex stochastic processes in a form Riesz fractional integrals. These results allow us obtain new class functional which generalizes known ones.

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 ...

Abstract We present unified versions of Minkowski-type fractional integral inequalities with the help operator based on a Mittag-Leffler function. These provide new as well already known inequalities.

Integral inequalities involving many fractional integral operators are used to solve various differential equations. In the present paper, we will generalize Hermite–Jensen–Mercer-type for an h-convex function via a Caputo–Fabrizio integral. We develop some novel inequalities. also identities differentiable mapping, and these be give estimates Some familiar results recaptured as special cases o...

In this paper, we study some new generalized 2D nonlinear Gronwall-Bellman type inequalities, which provide explicit bounds for unknown functions concerned, and are useful in the analysis of qualitative and quantitative properties for solutions to fractional differential and differential-integral equations. The presented inequalities are of new forms compared with the existing results so far in...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

This paper is devoted to establishing some functional generalizations of Hölder and reverse Hölder’s inequalities with local fractional integral introduced by Yang. Then, based on the obtained results, we derive related including Minkowski-type Dresher-type inequalities, which are extensions several existing inequalities.

The metric polytope metn is the polyhedron associated with all semimetrics on n nodes and defined by the triangle inequalities xij − xik − xjk ≤ 0 and xij + xik + xjk ≤ 2 for all triples i, j, k of {1, . . . , n}. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n ≤ 8 and, i...

The metric polytope metn is the polyhedron associated with all semimetrics on n nodes and defined by the triangle inequalities xij − xik − xjk ≤ 0 and xij + xik + xjk ≤ 2 for all triples i, j, k of {1, . . . , n}. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n ≤ 8 and, i...