Wavelet Methods for Solving Fractional-order Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelet Methods for Solving Fractional-order Dynamical Systems write by Kobra Rabiei. This book was released on 2022. Wavelet Methods for Solving Fractional-order Dynamical Systems available in PDF, EPUB and Kindle. In this dissertation we focus on fractional-order dynamical systems and classify these problems as optimal control of system described by fractional derivative, fractional-order nonlinear differential equations, optimal control of systems described by variable-order differential equations and delay fractional optimal control problems. These problems are solved by using the spectral method and reducing the problem to a system of algebraic equations. In fact for the optimal control problems described by fractional and variable-order equations, the variables are approximated by chosen wavelets with unknown coefficients in the constraint equations, performance index and conditions. Thus, a fractional optimal control problem is converted to an optimization problem, which can be solved numerically. We have applied the new generalized wavelets to approximate the fractional-order nonlinear differential equations such as Riccati and Bagley-Torvik equations. Then, the solution of this kind of problem is found using the collocation method. For solving the fractional optimal control described by fractional delay system, a new set of hybrid functions have been constructed. Also, a general and exact formulation for the fractional-order integral operator of these functions has been achieved. Then we utilized it to solve delay fractional optimal control problems directly. The convergence of the present method is discussed. For all cases, some numerical examples are presented and compared with the existing results, which show the efficiency and accuracy of the present method.
Wavelet Methods for Dynamical Problems
Wavelet Methods for Dynamical Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelet Methods for Dynamical Problems write by S. Gopalakrishnan. This book was released on 2010-03-17. Wavelet Methods for Dynamical Problems available in PDF, EPUB and Kindle. Employs a Step-by-Step Modular Approach to Structural ModelingConsidering that wavelet transforms have also proved useful in the solution and analysis of engineering mechanics problems, up to now there has been no sufficiently comprehensive text on this use. Wavelet Methods for Dynamical Problems: With Application to Metallic, Composite and Nano-co
Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations
Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations write by Santanu Saha Ray. This book was released on 2018-01-12. Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations available in PDF, EPUB and Kindle. The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.
Computational Fractional Dynamical Systems
Computational Fractional Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Fractional Dynamical Systems write by Snehashish Chakraverty. This book was released on 2022-11-15. Computational Fractional Dynamical Systems available in PDF, EPUB and Kindle. A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering. Covers various aspects of efficient methods regarding fractional-order systems Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering Provides a systematic approach for handling fractional-order models arising in science and engineering Incorporates a wide range of methods with corresponding results and validation Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.
Wavelets
Wavelets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelets write by Charles K. Chui. This book was released on 1997-01-01. Wavelets available in PDF, EPUB and Kindle. Wavelets continue to be powerful mathematical tools that can be used to solve problems for which the Fourier (spectral) method does not perform well or cannot handle. This book is for engineers, applied mathematicians, and other scientists who want to learn about using wavelets to analyze, process, and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. The only mathematically rigorous monograph written by a mathematician specifically for nonspecialists, it describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches, and provides information for problem solving, putting the reader at the forefront of current research.
