Boundedness of normalization generalized differential operator of fractional formal

Many authors have considered and investigated generalized fractional differential operators. The main object of this present paper is to define a new generalized fractional differential operator $mathfrak{T}^{beta,tau,gamma},$ which generalized the Srivastava-Owa operators. Moreover, we investigate of the geometric properties such as univalency, starlikeness, convexity for their normalization. Further, boundedness and compactness in some well known spaces, such as Bloch space for last mention operator also are considered. Our tool is based on the generalized hypergeometric function.

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

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this operator, we introduce an interesting subclass of functions which are analytic and univalent. Furthermore, this effort covers coefficient bounds, distortions theorem, radii of starlikeness, convexity, bounded turning, extreme points and integral means inequalities of functions belongs to this class. Finally, applications involving certain fractional operators are illustrated.

Integral transforms defined by a new fractional class of analytic function in a complex Banach space

In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.

Mixed solutions of monotone iterative technique for hybrid fractional differential equations

This paper concerns with a mathematical modelling of biological experiments, and its influence on our lives. Fractional hybrid iterative differential equations are equations that interested in mathematical model of biology. Our technique is based on the Dhage fixed point theorem. This tool describes mixed solutions by monotone iterative technique in the nonlinear analysis. This method is used to combine two solutions: lower and upper. It is shown an approximate result for the hybrid fractional differential equations iterative in the closed assembly formed by the lower and upper solutions.