Abstract
Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator mathfrak {J}_{m}(z) defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.
Highlights
The subject of fractional calculus has acquired significant popularity and major attention from several authors in various science due mainly to its direct involvement in the problems of differential equations in mathematics, physics, engineering and others for example Baskonus and Bulut (2015), Yin et al (2015) and Bulut (2016)
The fractional calculus has gained an interesting area in mathematical research and generalization of the operators and its useful utility to express the mathematical problems which often leads to problems to be solved see Yao et al (2015), Baskonus (2016) and Kumar et al (2016)
By using the technique of convolution or Hadamard product, Sălăgean (1981) defined the differential operator Dn of the class of analytic functions and it is well known as Salagean operator
Summary
The subject of fractional calculus (integral and derivative of any arbitrary real or complex order) has acquired significant popularity and major attention from several authors in various science due mainly to its direct involvement in the problems of differential equations in mathematics, physics, engineering and others for example Baskonus and Bulut (2015), Yin et al (2015) and Bulut (2016). These operators are play an important role in geometric function theory to define new generalized subclasses of analytic univalent and study their properties. By using the technique of convolution or Hadamard product, Sălăgean (1981) defined the differential operator Dn of the class of analytic functions and it is well known as Salagean operator.
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