Abstract
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.
Highlights
Research ArticleGeneralized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators
In 1903, the Swedish mathematician Mittag-Leffler [1] introduced the function Eα(z) as Eα (z) = ∞ ∑ n=0 Γ zn (1)where z ∈ C and Γ(s) is the gamma function; α ≥ 0.During the last century and due to its involvement in the problems of physics, engineering, and applied sciences, many authors defined and studied in their research papers different generalizations of Mittag-Leffler type function, namely, Eα,β(z) introduced by Wiman [2], Eαγ,β(z) stated by Prabhakar [3], Eαγ,qβ(z) defined and studied by Shukla and Prajapati [4], and Eαγ,δβ(z) investigated by Salim and Faraj [5]
This paper is devoted to study further properties of generalized Mittag-Leffler function Eαγ,δβ,qp associated with Weyl fractional integral and differential operators
Summary
Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators. This paper is devoted to study further properties of generalized Mittag-Leffler function Eαγ,,δβ,,qp associated with Weyl fractional integral and differential operators. A new integral operator Eγα,,δβ,,qp,w,∞ depending on Weyl fractional integral operator and containing Eαγ,,δβ,,qp(z) in its kernel is defined and studied, namely, its boundedness. Composition of Weyl fractional integral and differential operators with the new operator Eγα,,δβ,,qp,w,∞ is established
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