Related papers: Gruss-type inequality by mean of a fractional inte…

Some new Gruss type inequalities in inner product spaces and applications for integrals are given.

The median principle is applied for different integral inequalities of Gruss and Ostrowski type.

In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator.…

In this paper, we have established some generalized integral inequalities of Hermite-Hadamard-Fej\'er type for generalized fractional integrals. The results presented here would provide generalizations of those given in earlier works.

The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo fractional integral operator is used to establish the results.

In this paper, the author introduces the concept of the quasi-geometrically convex and defines a new identity for fractional integrals. By using of this identity, author obtains new estimates on generalization of Hadamard, Ostrowski and…

In this paper we propose and solve a generalization of the Bernoulli Differential Equation, by means of a generalized fractional derivative. First we prove a generalization of Gronwall's inequality, which is useful for studying the…

Some companions of Gruss inequality in inner product spaces and applications for integrals are given.

Sharp inequalitieis of Gruss type for Stieltjes integrals with application in numerical integration are provided.

We prove that a pointwise fractional Hardy inequality implies a fractional Hardy inequality, defined via a Gagliardo-type seminorm. The proof consists of two main parts. The first one is to characterize the pointwise fractional Hardy…

In this paper, we establish some new Hadamard type inequalities for s-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1 which has been proved by Sarikaya et al. in the paper [3].

Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…

Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu in [2]. In this study, firstly,…

In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…

Aim of this paper is to study the non-existence of global solutions of the fractional differential problem involving generalized Katugampola derivative. We utilize the test function method and fractional integration by parts formula to…

In this article, we presented some properties of the Katugampola fractional integrals and derivatives. Also we studied the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized $k-$Wright…

In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…