On a fractional class of analytic function defined by using a new operator

复域上由分数阶导数族指定的解析函数的一个新子类

A Novel Subclass of Analytic Functions Specified by a Family of Fractional Derivatives in the Complex Domain

本文利用复域上的一类分数阶导数算子，引入并研究了开单位圆盘上解析单叶函数的一个新子类$\mathcal{P}_{τ,μ}(k,δ,γ)$，该子类是$\mathbb{U}$ .特别地，对于$\mathcal{P}_{τ,μ}(k,δ,γ)$类中的函数，我们得到了包含上述分数阶导数算子的充分的系数不等式、偏差定理以及星形和凸性半径.此外，还指出了$\mathcal{P}_{τ,μ}(k,δ,γ)$类中函数的一些应用。

Harmonic univalent functions defined by q-calculus operators

The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal control, q-difference and q-integral equations, and also in the geometric function theory of complex analysis. In this article, for the first time, we apply certain q-calculus operators to complex harmonic functions and obtain sharp coefficient bounds, distortion theorems and covering results.

Wiman-Valiron方法用于分数导数及线性分数微分方程中α-解析解的精确增长估计

Wiman-Valiron method for fractional derivatives and sharp growth estimates of $α$-analytic solutions for linear fractional differential equations

本文通过扩展Wiman-Valiron理论，研究了分数微分方程中α-解析解的精确增长估计，并推广了Kochubei的结果。

关于由分数阶导数定义的一类调和函数

On certain classes of harmonic functions defined by the fractional derivatives

本文引入了两个新的复值调和多叶函数类$\mathcal{H}\mathcal{M}(β, λ, k, ν)$和$\overline{\mathcal{H}\mathcal{M}} (β, λ, k, ν)$，它们满足条件$f = h + \overline g$，其中$h$和$g$在单位圆盘$\mathcal{D} = \{z : |z| < 1\}.$中解析，并确定了这类函数在$\mathcal{H}\mathcal{M}(β, λ, k, ν)$类中的充分系数条件和函数$f$在$\overline{\mathcal{H}\mathcal{M}}(β, λ, k, ν)$类中的充分必要系数条件.我们研究了这类调和函数族的包含关系、偏差定理、极值点、凸组合等有趣的性质。