Upper bound for functions of bounded turning

For normalized analytic functions in the unit disk, we consider subclasses of bounded turning. The geometric representation is introduced, the radii of convexity (close to convex) are calculated and some subordination relations are suggested. Moreover, the upper bound of the pre-Schwarzian norm for these functions is computed

Approximate solutions for non-linear iterative fractional differential equations

This paper establishes approximate solution for non-linear iterative fractional differential equations: dyv(s)/dsy = ℵ(s,v,v(v)), where γ ∈ (0, 1], s ∈ I := [0, 1]. Our method is based on some convergence tools for analytic solution in a connected region. We show that the suggested solution is unique and convergent by some well known geometric functions

Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method

In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations

Jack's lemma for certain subclasses of analytic functions defined by a new fractional linear operator

The theory of functional operator has been employed in several areas of mathematics, especially in the geometric function theory in the open unit disk. By utilizing the Moment-Generating function, we define a new fractional linear operator in the open unit disk. We discuss some geometric properties of this operator on some subclasses by applying the concept Jack’s lemma

Application of modified complex Tremblay operator

In this paper, we introduce a new fractional integral operator defined by modified fractional derivative Tremblay operator of analytic functions and show that the univalence of this integral operator is preserved under certain sufficient conditions in complex domain ℂ

A note on the class of functions with bounded turning

We consider subclasses of functions with bounded turning for normalized analytic functions in the unit disk. The geometric representation is introduced, some subordination relations are suggested, and the upper bound of the pre-Schwarzian norm for these functions is computed. Moreover, by employing Jack's lemma, we obtain a convex class in the class of functions of bounded turning and relations with other classes are posed

A Mathematical Model of Cloud Computing in the Economic Fractional Dynamic System

Computing is experiencing much change from client/server to the cloud. The interest for cloud infrastructures is not only introducing in the business domain, but likewise encompasses to government activities. In this work, we suggest a new dynamic system, equilibrium of cloud computing based on fractional calculus. In our preparation, each agent (i.e., each company or government agency) determines between going to appliance the customary on-site computing pattern and acting to the cloud computing model. In this model, separately agent will optimize an entire cost that involves of two mechanisms: the cost of implementing the cloud computing pattern and the effort cost of moving to the cloud computing pattern. We shall impose various types of two-dimensional fractional systems. The method of finding the solution is subjected to bifurcation and bifurcation boundaries to perform a good result in the cloud computing. This method is generalized to the fractional calculus. Therefore, the outcome lets us to training the dynamic evolution of the density of cloud computing

Generalized Φ-dichotomous linear part for a class of generalized differential equations

A dichotomy: ordinary or exponential, is a category of conditional stability. In this disquisition, we deal with nonlinear fractional differential equations (NFDE) involving generalized Φ-exponential and Φ-ordinary dichotomous (in the sense of fractional calculus) linear part in a Banach space. By employing of the Banach fixed point principle, the satisfactory conditions are located for the existence of Φ-bounded outcomes of these equations in the real case

Improved Image Splicing Forgery Detection by Combination of Conformable Focus Measures and Focus Measure Operators Applied on Obtained Redundant Discrete Wavelet Transform Coefficients

The image is the best information carrier in the current digital era and the easiest to manipulate. Image manipulation causes the integrity of this information carrier to be ambiguous. The image splicing technique is commonly used to manipulate images by fusing different regions in one image. Over the last decade, it has been confirmed that various structures in science and engineering can be demonstrated more precisely by fractional calculus using integrals or derivative operators. Many fractional-order-based techniques have been used in the image-processing field. Recently, a new specific fractional calculus, called conformable calculus, was delivered. Herein, we employ the combination of conformable focus measures (CFMs), and focus measure operators (FMOs) in obtaining redundant discrete wavelet transform (RDWT) coefficients for improving the image splicing forgery detection. The process of image splicing disorders the content of tampered image and causes abnormality in the image features. The spliced region's boundaries are usually blurring to avoid detection. To make use of the blurred information, both CFMs and FMOs are used to calculate the degree of blurring of the tampered region's boundaries for image splicing detection. The two public image datasets IFS-TC and CASIA TIDE V2 are used for evaluation of the proposed method. The obtained results of the proposed method achieved accuracy rate 98.30% for Cb channel on IFS-TC image dataset and 98.60% of the Cb channel on CASIA TIDE V2 with 24-D feature vector. The proposed method exhibited superior results compared with other image splicing detection methods. © 2019 by the authors