A new class of analytic functions associated with the Ruscheweyh derivatives

Some Geometric Properties of Analytic Functions Involving a New Fractional Operator

“…We note that the fractional operator D ν,0 0 defined by (1.2) is precisely the Ruscheweyh derivative operator R ν of order ν (ν > −1) and D 0,0 λ is the fractional differintegral operator Ω λ z of order λ (−∞ < λ < 2) , while D 0,n 0 = D n and D 1−λ,n λ = D n+1 are the Sȃlȃgean operators, respectively, of order n and n + 1 (n ∈ N 0 ) . There are numerous results in the literature on the Geometric Function Theory which are based on the use of the Ruscheweyh, Sȃlȃgean, and the fractional differintegral operators (see, for instance, the works in [6][7][8][9][10]13,17,[19][20][21][22][23]26,28,29]; see also [27] (and the references cited therein).…”