q–differ-integral operator on p–valent functions associated with operator on Hilbert space

Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.

Color Edge Detection Using Multidirectional Sobel Filter and Fuzzy Fusion

A new model is proposed in this paper on color edge detection that uses the second derivative operators and data fusion mechanism.The secondorder neighborhood shows the connection between the current pixel and the surroundings of this pixel.This connection is for each RGB component color of the input image.Once the image edges are detected for the three primary colors:red,green,and blue,these colors are merged using the combination rule.Then,the final decision is applied to obtain the segmentation.This process allows different data sources to be combined,which is essential to improve the image information quality and have an optimal image segmentation.Finally,the segmentation results of the proposed model are validated.Moreover,the classification accuracy of the tested data is assessed,and a comparison with other current models is conducted.The comparison results show that the proposed model outperforms the existing models in image segmentation.

New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory

The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.

3D Fractals, Axiom of Algebra (Δn)n = +1

After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.

Existence of positive solutions for integral boundary value problem of fractional differential equations

In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.

APPLICATIONS OF WAVELET GALERKIN FEM TO BENDING OF BEAM AND PLATE STRUCTURES

In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavelet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.

Laguerre reproducing kernel method in Hilbert spaces for unsteady stagnation point ow over a stretching/shrinking sheet

This paper investigates the nonlinear boundary value problem resulting from the exact reduction of the Navier-Stokes equations for unsteady magnetohydrodynamic boundary layer flow over the stretching/shrinking permeable sheet submerged in a moving fluid.To solve this equation,a numerical method is proposed based on a Laguerre functions with reproducing kernel Hilbert space method.Using the operational matrices of derivative,we reduced the problem to a set of algebraic equations.We also compare this work with some other numerical results and present a solution that proves to be highly accurate.

Numerical Solution of Klein/Sine-Gordon Equations by Spectral Method Coupled with Chebyshev Wavelets

The basic aim of this paper is to introduce and describe an efficient numerical scheme based on spectral approach coupled with Chebyshev wavelets for the approximate solutions of Klein-Gordon and Sine-Gordon equations. The main characteristic is that, it converts the given problem into a system of algebraic equations that can be solved easily with any of the usual methods. To show the accuracy and the efficiency of the method, several benchmark problems are implemented and the comparisons are given with other methods existing in the recent literature. The results of numerical tests confirm that the proposed method is superior to other existing ones and is highly accurate

Using wavelet multi-resolution nature to accelerate the identification of fractional order system

Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system identification, the leastsquares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.

A Unified FastMemory-Saving Time-SteppingMethod for Fractional Operators and Its Applications

Time-dependent fractional partial differential equations typically require huge amounts of memory and computational time,especially for long-time integration,which taxes computational resources heavily for high-dimensional problems.Here,we first analyze existing numerical methods of sum-of-exponentials for approximating the kernel function in constant-order fractional operators,and identify the current pitfalls of such methods.In order to overcome the pitfalls,an improved sum-of-exponentials is developed and verified.We also present several sumof-exponentials for the approximation of the kernel function in variable-order fractional operators.Subsequently,based on the sum-of-exponentials,we propose a unified framework for fast time-stepping methods for fractional integral and derivative operators of constant and variable orders.We test the fast method based on several benchmark problems,including fractional initial value problems,the time-fractional Allen-Cahn equation in two and three spatial dimensions,and the Schr¨odinger equation with nonreflecting boundary conditions,demonstrating the efficiency and robustness of the proposed method.The results show that the present fast method significantly reduces the storage and computational cost especially for long-time integration problems.