Some results on the generalized Mittag-Leffler function operator

Abstract

This paper is devoted to the study of a generalized Mittag-Leffler function operator introduced by Shukla and Prajapati (J. Math. Anal. Appl. 336:797-811, 2007

Integral representations of Mittag-Leffler function on the positive real axis

“…for t > 0 and any real number σ satisfying the condition σ ≥ σ 0 > 0, where σ 0 is large enough that . It is worthwhile to mention that the detail treatment of the similar study can be found in [28,30].…”

Modified Double Zeta Function and Its Properties

“…Due to great potential and significant role of special functions especially hypergeometric functions in various problems occurring in mathematical physics, engineering [8] [9], the author has motivated to further investigate the topic. Several generalizations of hypergeometric functions have been made by many authors [10] [11]. Recently Rao [12] defined Wright type generalized hypergeometric function via fractional calculus.…”

Differential Subordination with Hadamard Product of Generalized k-Mittag-Leffler Function and a Class of Function

“…Several properties of Mittag-Leffler function and generalized Mittag-Leffler function can be found e.g. in [2], [5], [6], [7], [8], [10], [15], [16], [17], [18], [26], [27] and [28].…”