Jitendra Daiya

Inequalities associated with Čebyšev functional for Saigo fractional integration operator

By making use of Saigo operator of fractional integration, some integral inequalities for the Čebyšev functional in the case of two synchronous functions are investigated which provide extensions in several directions of earlier results given for Riemann–Liouville operator.

FRACTIONAL DIFFERENTIATION OF THE PRODUCT OF APPELL FUNCTION F 3 AND MULTIVARIABLE H-FUNCTIONS

Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and useful- ness in many branches of science, engineering, technology, earth sciences and so on. Saigo et al. (9) evaluated the fractional integrals of the product of Appell function of the third kernel F3 and multivariable H-function. In this sequel, we aim at deriving the generalized fractional differentia- tion of the product of Appell function F3 and multivariable H-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional dif- ferentiation, for example, Riemann-Liouville, Erdelyi-Kober and Saigo operators, associated with multivariable H-function and Appell function F3 are shown to be deduced as special cases of our findings.

New fractional integral inequalities associated with pathway operator

This paper deals with the derivation of certain integral inequalities involving fractional integral operators of Chebyshev type by an application of the pathway fractional integral operator. The results obtained are of general character and provide extension of results given by Belarbi and Dahmani.

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

Abstract This paper deals with the derivation of certain new Pőlya-Szegő type inequalities by making use of the Saigo fractional integral operator. The results obtained cover the same kind of conclusions in the case of Riemann-Liouville and Erdélyi-Kober fractional integral operators.