Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators

This paper is devoted to study further properties of generalized Mittag-Leffler functionEα,β,pγ,δ,qassociated with Weyl fractional integral and differential operators. A new integral operatorℰα,β,p,w,∞γ,δ,qdepending on Weyl fractional integral operator and containingEα,β,pγ,δ,q(z)in its kernel is defined and studied, namely, its boundedness. Also, composition of Weyl fractional integral and differential operators with the new operatorℰα,β,p,w,∞γ,δ,qis established.

The two dimensional generalized Weyl fractional calculus and special functions

The object of this present paper is to derive a relation between the two dimensional I-transform involving a general class of polynomials and the Weyl type two dimensional Saigo operators of fractional integration. The results derived here are general in nature and include the results given earlier by Saigo, Saxena and Ram [10],Saxena and Ram [8], Saxena and Kiryakova [9] and Chaurasia and Srivastava [12].

Two-dimensional generalized Weyl fractional calculus pertaining to two-dimensional $ \overline{H} $-transforms

The aim of this paper is to establish a relation between the two-dimensional $ \overline{H} $-transform involving a general polynomials and the Weyl type two-dimensional Saigo operator of fractional integration.