In this work, we use the generalized exponential function in the fractional-order domain to define generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. It is clearly shown that trigonometric functions and trigonometric identities in the transient-time ...

Understanding trigonometry relational system is a school mathemat-ics demanding topic. The angle, the unit circle and trigonometric functions are its foundational notions. Trigonometric contents mean-ing their understanding involve these three concepts re-lationships. This research aims to deepen in pre-service teachers’ about function when converting notions between two repre-sentation systems...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

In the recent years, many direct methods have been developed to construct travelling wave solutions to the nonlinear partial differential equations (NLPDEs), such as the trigonometric function series method [1, 2], the modified mapping method and the extended mapping method [3], the modified trigonometric function series method [4], the dynamical system approach and the bifurcation method [5], ...

The paper continues the authors ’ research on evaluation of trigonometric sums an algebraic grid with weights. case arbitrary weight function infinite order is considered. For parameter

In this paper, the modified exp-function method is used to seek generalized wave solutions of Kudryashov-Sinelshchikov equation. As a result, some new types of exact traveling wave solutions for arbitrary α, β are obtained which include exponential function, hyperbolic function and trigonometric function. The related results are extend. Obtained results clearly indicate the reliability and effi...

Introduction/purpose: The aim of this article is to establish integral transforms the generalized Lommel-Wright function. Methods: These are expressed in terms Wright Hypergeometric Results: Integrals involving trigonometric, Bessel function and Struve functions obtained. Conclusions: Various interesting as consequence method

In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet tran...