Fractional Ostrowski Type Inequalities Research Articles

Fractional Ostrowski type inequalities for differentiable harmonically convex functions

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

Fractional Ostrowski Type Inequalities via Generalized Mittag–Leffler Function

If we study the theory of fractional differential equations then we notice the Mittag–Leffler function is very helpful in this theory. On the contrary, Ostrowski inequality is also very useful in numerical computations and error analysis of numerical quadrature rules. In this paper, Ostrowski inequalities with the help of generalized Mittag–Leffler function are established. In addition, bounds of fractional Hadamard inequalities are given as straightforward consequences of these inequalities.

Fractional Ostrowski type inequalities for bounded functions

We first establish some results involving Riemann–Liouville fractional integrals for partially differentiable functions. Then we obtain some fractional Ostrowski type inequalities for functions in class of functions L_{p}, L_{infty } and L_{1}, respectively. We also give some midpoint type inequalities as special cases of our main results.

Fractional Ostrowski type inequalities for functions of bounded variaton with two variables

Fractional Ostrowski type inequalities for functions of bounded variaton with two variables

Fractional Ostrowski type inequalities for functions whose modulus of the first derivatives are prequasi-invex

Abstract In this paper, we establish fractional Ostrowski inequalities for functions whose modulus of the first derivatives are prequasi-invex. Midpoint inequalities are also derived.

Fractional Ostrowski type inequalities for functions whose mixed derivatives are prequasiinvex functions

In this paper, the class of co-ordinated prequasiinvex functions is introduced, a new identity involving functions of two variable is establshed, some new fractional Ostrowski type inequalities are derived.

Some Hermite–Hadamard and Ostrowski type inequalities for fractional integral operators with exponential kernel

We rstly establish Hermite–Hadamard type integral inequalities for fractional integral operators. Secondly, we give new generalizations of fractional Ostrowski type inequalities through convex functions via Hölder and power means inequalities. In accordance with this purpose, we use fractional integral operators with exponential kernel.

Fractional Ostrowski Type Inequalities for Functions Whose Mixed Derivatives are Prequasiinvex and alpha-Prequasiinvex Functions

In this paper, the authors introduce two new classes of generalized convexfunctions of two independent variables, and establish a new integralidentity, from which they derive some new fractional Ostrowski's integralinequalities for functions whose second derivatives are in these new classesof functions.

Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality

Abstract In this paper, we establish fractional Ostrowski’s inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality.

Fractional Ostrowski type inequalities for functions whose derivatives are s-preinvex

In this paper, some new fractional Ostrowski's inequalities for functions whose first derivatives in absolute value are $MT$-preinvex are established, mid point inequalities are also derived.

Fractional Ostrowski Type Inequalities for Functions Whose First Derivatives Are s-Preinvex in the Second Sense

In this paper, we establish an fractional identity. Using this new identity we derives some fractional Ostrowski’s inequalities for functions whose first derivatives are s-preinvex in the second sense.

Fractional Representation Formulae Under Initial Conditions and Fractional Ostrowski Type Inequalities

AbstractHere we present very general fractional representation formulae for a function in terms of the fractional Riemann-Liouville integrals of different orders of the function and its ordinary derivatives under initial conditions. Based on these, we derive general fractional Ostrowski type inequalities with respect to all basic norms.

Multivariate fractional Ostrowski type inequalities

Optimal upper bounds are given for the deviation of a value of a multivariate function of a fractional space from its average, over convex and compact subsets of R N , N ≥ 2 . In particular we work over rectangles, balls and spherical shells. These bounds involve the supremum and L ∞ norms of related multivariate fractional derivatives of the function involved. The inequalities produced are sharp, namely they are attained. This work has been motivated by the works of Ostrowski [A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funcktion von ihrem Integralmittelwert, Commentarii Mathematici Helvetici 10 (1938) 226–227], 1938, and of the author [G.A. Anastassiou, Fractional Ostrowski type inequalities, Communications in Applied Analysis 7 (2) (2003) 203–208], 2003.