Local Fractional Integral Transforms And Their Applications
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Local Fractional Integral Transforms And Their Applications
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Author : Xiao Jun Yang
language : en
Publisher: Academic Press
Release Date : 2015-10-22
Local Fractional Integral Transforms And Their Applications written by Xiao Jun Yang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.
Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods
Integral Transforms And Their Applications
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Author : Lokenath Debnath
language : en
Publisher: CRC Press
Release Date : 2014-11-07
Integral Transforms And Their Applications written by Lokenath Debnath and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.
Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic
General Fractional Derivatives
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Author : Xiao-Jun Yang
language : en
Publisher: CRC Press
Release Date : 2019-05-10
General Fractional Derivatives written by Xiao-Jun Yang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
Integral Transforms And Their Applications
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Author : Lokenath Debnath
language : en
Publisher: CRC Press
Release Date : 1995-07-03
Integral Transforms And Their Applications written by Lokenath Debnath and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-03 with Mathematics categories.
Integral Transforms and Their Applications, provides a systematic , comprehensive review of the properties of integral transforms and their applications to the solution of boundary and initial value problems. Over 750 worked examples, exercises, and applications illustrate how transform methods can be used to solve problems in applied mathematics, mathematical physics, and engineering. The specific applications discussed include problems in differential, integral, and difference equations; electric circuits and networks; vibrations and wave propagation; heat conduction; fractional derivatives and fractional integrals; dynamical systems; signal processing; quantum mechanics; atmosphere and ocean dynamics; physical chemistry; mathematical biology; and probability and statistics. Integral Transforms and Their Applications includes broad coverage the standard material on integral transforms and their applications, along with modern applications and examples of transform methods. It is both an ideal textbook for students and a sound reference for professionals interested in advanced study and research in the field.
Generalized Fractional Calculus And Applications
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Author : Virginia S Kiryakova
language : en
Publisher: CRC Press
Release Date : 1993-12-27
Generalized Fractional Calculus And Applications written by Virginia S Kiryakova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-27 with Mathematics categories.
In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.
Fractional Integral Transforms
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Author : Ahmed I. Zayed
language : en
Publisher: CRC Press
Release Date : 2024-03-28
Fractional Integral Transforms written by Ahmed I. Zayed and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-28 with Mathematics categories.
Fractional Integral Transforms: Theory and Applications presents over twenty-five integral transforms, many of which have never before been collected in one single volume. Some transforms are classic, such as Laplace, Fourier, etc, and some are relatively new, such as the Fractional Fourier, Gyrator, Linear Canonical, Special Affine Fourier Transforms, as well as, continuous Wavelet, Ridgelet, and Shearlet transforms. The book provides an overview of the theory of fractional integral transforms with examples of such transforms, before delving deeper into the study of important fractional transforms, including the fractional Fourier transform. Applications of fractional integral transforms in signal processing and optics are highlighted. The book’s format has been designed to make it easy for readers to extract the essential information they need to learn the about the fundamental properties of each transform. Supporting proofs and explanations are given throughout. Features Brings together integral transforms never before collected into a single volume A useful resource on fractional integral transforms for researchers and graduate students in mathematical analysis, applied mathematics, physics and engineering Written in an accessible style with detailed proofs and emphasis on providing the reader with an easy access to the essential properties of important fractional integral transforms Ahmed I. Zayed is a Professor of Mathematics at the Department of Mathematical Sciences, DePaul University, Chicago, and was the Chair of the department for 20 years, from 2001 until 2021. His research interests varied over the years starting with generalized functions and distributions to sampling theory, applied harmonic analysis, special functions and integral transforms. He has published two books and edited seven research monographs. He has written 22 book chapters, published 118 research articles, and reviewed 173 publications for the Mathematical Review and 81 for the Zentralblatt für Mathematik (zbMath). He has served on the Editorial Boards of 22 scientific research journals and has refereed over 200 research papers submitted to prestigious journals, among them are IEEE, SIAM, Amer. Math. Soc., Math Physics, and Optical Soc. Journals.
Integral Transforms And Their Applications
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Author : Brian Davies
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-02
Integral Transforms And Their Applications written by Brian Davies and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-02 with Mathematics categories.
This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Chapter I is largely new, covering introductory aspects of complex variable theory. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools. Around 400 problems are accompanied in the text. It will be useful for graduate students and researchers working in mathematics and physics.
An Introduction To Integral Transforms And Their Applications
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Author : Olga Moreira
language : en
Publisher: Arcler Press
Release Date : 2018-12
An Introduction To Integral Transforms And Their Applications written by Olga Moreira and has been published by Arcler Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12 with Mathematics categories.
The Fourier, Laplace, Mellin, Hilbert, and Hankel transforms are classic examples of integral equations with numerous applications in several fields of science and engineering, When mapping a function from one domain into another, integral transforms provide an elegant solution for many mathematical problems that are algebraically difficult to solve in their original domain but of simpler solution in the target domain. The Fourier transform, for example, maps an original signal (represented by a function of time) into its coresponding power spectrum in the frequency domain. Therefore, the Fourier transform plays an essential role in data analysis of periodic signals, decomposing the incoming signal into the frequencies that its consists of. The Laplace transform converts a convolution in the original domain into a simple multiplication in the target domain. This transform has extensive applications in the fields of engineering and physics research involving the analysis of time-invariant systems in which the output signal is calculated as the convolution between the impulse response and the input signal. Many applications of probability theory also rely on integral transforms, such as statistics that are based on kernel functions. This book is a collection of contemporary open access articles which highlight the importance of integral transforms and their applications. In particular, three topics are discussed: Analysis of generalized functions for integral transform and their properties; Methods for solving the Cauchy problem (initial value or boundary problems) for space-time partial differential equations; Applications of integral transform, including fractional methods, to solving systems of differential equations in physics, signal processing, quantum mechanics and mechanical engineering. The generalization of global estimates for various integral transforms is discussed by Vindas & Estrada (2006). The properties kernels of Laplace-typed integral transform and q-Laplace transforms were studied by Kim (2017) and Naik & Haubold (2016), respectively. Transform methods for convex polygons are derived by Crowdy (2015); the analysis of singular integral equations (Li, 2017); matrix integral transforms (Yaremko & Yaremko, 2016), Sumudu transforms (Rahman & Ahmad, 2015) are also included in this book. The remaining content of this book focuses on applications of the integral transform as a method for solving various differential equations. This book is mainly addressed to physicists, advanced undergraduate and graduate students in the Natural Sciences and Mechanical Engineering. Book jacket.
Special Functions In Fractional Calculus And Engineering
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2023-06-29
Special Functions In Fractional Calculus And Engineering written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-29 with Technology & Engineering categories.
Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.
Integral Transforms And Their Applications
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Author : K. P. Das
language : en
Publisher:
Release Date : 2019-04-30
Integral Transforms And Their Applications written by K. P. Das and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-30 with Mathematics categories.
Describes four important integral transforms: Fourier transform, Laplace transform, Mellin transform, and Hankel transform, together with their application. These four integral transforms have been defined and their inversion formulas have been derived. They have been used in finding the solution of many physical problems. These problems include evolution of some definite integrals, integral equations involving Fourier kernel, solution of some partial differential equations with given initial and boundary conditions, which are of importance in mathematical physics.