The integration of certain product involving special functions

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

Integration formulas for the conditional transform involving the first variation

In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

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...

Convergence of product integration method applied for numerical solution of linear weakly singular Volterra systems

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

Subordination and Super Ordination Results Involving Certain Convolution Operators