Saigo Fractional Integral Operator Research Articles

Applications of $ q- $Ultraspherical polynomials to bi-univalent functions defined by $ q- $Saigo's fractional integral operators

<abstract><p>This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing $ q- $Ultraspherical polynomials under $ q- $Saigo's fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated.</p></abstract>

Composition Formula for Saigo Fractional Integral Operator Associated with V-Function

In this study, we form integral formulas for Saigo’s hypergeometric integral operator involving V-function. Corresponding assertions for the classical Riemann–Liouville (R-L) and Erdélyi–Kober (E-K) fractional integral operator are extrapolated. Also, by putting in the transformations of Beta and Laplace, we can establish their composition formulas. By selecting the appropriate parameter values, the V-function may be reduced to a variety of functions, including the exponential function, Mittag–Leffler, Lommel, Struve, Wright’s generalized Bessel function, and Bessel and generalized hypergeometric function.

On generalized fractional integral operator associated with generalized Bessel-Maitland function

<abstract><p>In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.</p></abstract>

Modified Saigo fractional integral operators involving multivariable H-function and general class of multivariable polynomials

In this paper, we establish modified Saigo fractional integral operators involving the product of a general class of multivariable polynomials and the multivariable H-function. The results established here are of general nature and provide extension of some results obtained recently by Saxena et al.

Inequalities for n-class of functions using the Saigo fractional integral operator

The role of fractional integral operators can be found as one of the best ways to generalize the classical inequalities. In this paper, we use the Saigo fractional integral operator to produce some inequalities for a class of n-decreasing positive functions. The results are more general than the available classical results in the literature.

Some integral inequalities involving Saigo fractional integral operators

In this paper, the Saigo fractional integral operator is used to generate some new integral inequalities. By using the Saigo fractional integral operator, we also generate new classes of integral inequalities using a family of n positive functions defined on [a, b].

On some w-weighted fractional integral inequalities involving the Saigo fractional integral operators

On some w-weighted fractional integral inequalities involving the Saigo fractional integral operators

On generalization of an integral inequality and its applications

In this paper, we give generalization of an integral inequality. We find its applications in fractional calculus by involving different kinds of fractional integral operators, for example Riemann–Liouville fractional integral, Caputo fractional derivative, Canavati fractional derivative and Widder derivative, Saigo fractional integral operator, etc.

Some new Chebyshev and Grüss-type integral inequalities for Saigo fractional integral operators and their q-analogues

By making use of Saigo fractional integral operators, we establish some new results of the fractional Chebyshev and Grüss-type integral inequalities. Furthermore, the q-extensions of the main results are also presented. Our results in special cases yield some of the recent results on Chebyshev and Grüss-type integral inequalities.

New Fractional Inequalities Involving Saigo Fractional Integral Operator

The aim of this paper is to obtain some new results related to Minkowski fractional integral inequality and other integra l inequalities using Saigo fractional integral .

Certain Grüss type inequalities involving the generalized fractional integral operator

Abstract A remarkably large number of Grüss type fractional integral inequalities involving the special function have been investigated by many authors. Very recently, Kalla and Rao (Matematiche LXVI(1):57-64, 2011) gave two Grüss type inequalities involving the Saigo fractional integral operator. Using the same technique, in this paper, we establish certain new Grüss type fractional integral inequalities involving the Gauss hypergeometric function. Moreover, we also consider their relevances for other related known results. MSC: 26D10, 26A33.

On Some Grüss-Type Fractional Inequalities Using Saigo Fractional Integral Operator

The main aim of this paper is to establish some new fractional integral inequalities of Grüss-type via the Saigo fractional integral operator.

Diaz-Metcalf and Pólya-Szegő type inequalities associated with Saigo fractional integral operator

Diaz-Metcalf and Pólya-Szegő type inequalities associated with Saigo fractional integral operator

Chebyshev type inequalities for the Saigo fractional integrals and their q-analogues

The aim of the present paper is to obtain certain new integral inequalities involving the Saigo fractional integral operator. It is also shown how the various inequalities considered in this paper admit themselves of q-extensions which are capable of yielding various results in the theory of q-integral inequalities.

A Certain Class of Multivalent Prestarlike Functions Defined by Dziok-Srivastava Linear Operator

In this paper, we have introduced a new class of p-valent prestarlike functions with negative coefficients defined by Dziok- Srivastava linear operator. Growth and distortion theorems have been proved in terms of Saigo fractional integral operator. Class preserving integral operator and radius of convexity of this class have also been investigated. Some special cases of the results have also been proved. Keywords: Prestarlike functions; Dziok-Srivastava linear operator; Fractional integral operator.