Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

The aim of this paper is to introduce and investigate new subclasses of regular functions defined in . The coefficients estimate and  for functions in these subclasses are determined. Many of new and known consequences are shown as particular cases of our outcomes.

This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabi

In this paper, we show many conclusions on the Quasi-Hadamard products of new Subclass of analytic functions of β-Uniformly univalent function  defined by Salagean q-differential operator.

     In this study, an efficient novel technique is presented to obtain a more accurate analytical solution to nonlinear pantograph differential equations. This technique combines the Adomian decomposition method (ADM) with the homotopy analysis method concepts (HAM). The whole integral part of HAM is used instead of an integral part of ADM approach to get higher accurate results. The main advantage of this technique is that it  gives a large and more extended convergent region of iterative approximate solutions for long time intervals that rapidly converge to the exact solution. Another advantage is capable of providing a continuous representation of the approximate solutions, which gives  better information over whole time interv

We presented in this paper a new class containing analytic univalent functions defined on unit disk. We obtained many geometric properties , like , coefficient inequality , distortion and growth theorems, convolution property, convex set, arithmetic mean and radius of starlikness and convexity by using Gaussian hypergeometric function for the class

       In this paper we offer two new subclasses of an open unit disk of r-fold symmetric bi-univalent functions. The Taylor-Maclaurin coefficients  have their coefficient bounds calculated. Furthermore, for functions in , we have solved Fekete-  functional issues. For the applicable classes, there are also a few particular special motivator results.

         In the present paper, the authors introduce and investigates two new subclasses and,  of the class k-fold bi-univalent functions in the open unit disk. The initial coefficients for all of the functions that belong to them were determined, as well as the coefficients for functions that belong to a field determining these coefficients requires a complicated process. The bounds for the initial coefficients and are contained among the remaining results in our analysis are obtained. In addition, some specific special improver results for the related classes are provided.

In this paper, we illustrate how to use the generalized homogeneous -shift operator  in generalizing various well-known q-identities, such as Hiene's transformation, the q-Gauss sum, and Jackson's transfor- mation. For the polynomials , we provide another formula for the generating function, the Rogers formula, and the bilinear generating function of the Srivastava-Agarwal type. In addition, we also generalize the extension of both the Askey-Wilson integral and the Andrews-Askey integral.

     In this paper , certain subclass of harmonic multivalent function defined in the exterior of the unit disk by used generalize hypergeometric functions is introduced . In This study an attempting have been made to investigate several geometric properties such as coefficient property , growth bounds , extreme points , convolution property , and  convex linear combination .