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 operat...

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...

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

M. Saigo [Math. Rep. Coll. Gen. Educ., Kyushu Univ., 11 (1978) 135-143] has defined a pair of fractional integral operators and fractional derivatives involving generalizd hypergeometric function. The aim of present paper is to define their q-analogues. First, we define a pair of q-analogues of Saigo’s fractional integral operators and establish some results for it. Next, we define a pair of q-...

Fractional differential calculus have recently been addressed by many researchers of various fields of science and engineering such as physics, chemistry, biology, economics, control theory, and biophysics, etc. [1-4]. In particular, the existence of solutions to fractional boundary value problems is under strong research recently, see [5-7] and references therein. The fractional q-difference c...

Making use of a differential operator the author investigate the various impartant properties and characteristics of the subclass Tj(n,m, p, q, α) (p, j,m ∈ N = {1, 2, . . .}, q, n ∈ N0 = N ∪ {0}, 0 ≤ α < p − q) of p-valently analytic functions with negative coefficients. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered.

Using the Wright’s generalized hypergeometric function, we investigate a class W (q, s;A,B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W (q, s;A,B, λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) o...