In this paper, a differential operator is used to generate a subclass of analytic and univalent functions with positive coefficients. The studied class of the functions includes:  

which is defined in the open unit disk  satisfying the following condition

This leads to the study of properties such as coefficient bounds, Hadamard product, radius of close –to- convexity, inclusive properties, and (n, τ) –neighborhoods for functions belonging to our class.

          We obtain the coefficient estimates, extreme points, distortion and growth boundaries, radii of starlikeness, convexity, and close-to-convexity, according to the main purpose of this paper.

Despite the importance of this term in linguistics and rhetoric ancient and modern literary forms in general, is that it is possible to use in clarifying the foundations of the relationship hidden and manifest between shapes in models art adjacent or successive spatially, as the artwork plastic in general and sculpture in particular consists of formal structure somewhat similar to the structure in any language text and we can decode these blades structure and analyze the implications and come to their meanings and re-read and interpreted under the guidance of the concepts and techniques of neighboring developed primarily for linguistic analysis of texts or launched from their references. This split search to four chapters included the fi

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

In this paper we introduced a new type of integrals based on binary element sets “a generalized integral of Shilkret and Choquet integrals” that combined the two kinds of aggregation functions which are Shilkret and Choquet integrals. Then, we gave some properties of that integral. Finally, we illustrated our integral in a numerical example.
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 In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.