We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fraction...

In this paper, we establishes certain new weighted Young and P?lya-Szeg?-type inequalities involving Marichev-Saigo-Maeda fractional integral operators. Meanwhile, corresponding Cauchy-Schwarz type inequalities, Shisha-Mond Diaz-Metcalf for operators are also obtained. As applications, some estimates Chebyshev-type with two unknown functions presented. The main results of paper more general inc...

This evaluation can be found in standard tables of series, such as those of E. R. Hansen [44, p. 262, eq. (30.1.2)], L. B. W. Jolly [56, pp. 102–103, eq. (352)], and A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev [70, p. 646, eq. 6]. We do not know who first proved (1.1), but several proofs exist. If we replace the power 2 on the left side by an arbitrary positive even power, finding an e...

Abstract We consider a general class of integro-differential evolution equations which includes the governing equation generalized grey Brownian motion and time- space-fractional heat equation. present relation between parameters distribution underlying stochastic processes, as well discuss different classes processes providing solutions these equations. For subclass equations, containing Maric...