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Author : Xiao Jun Yang
Publisher : Unknown
Page : 0 pages
File Size : 47,7 Mb
Release : 2015
Category : Electronic
ISBN : OCLC:956678553
Author : Xiao Jun Yang,Dumitru Baleanu,H. M. Srivastava
Publisher : Academic Press
Page : 262 pages
File Size : 47,5 Mb
Release : 2015-10-22
Category : Mathematics
ISBN : 9780128040324
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
Author : Lokenath Debnath,Dambaru Bhatta
Publisher : CRC Press
Page : 806 pages
File Size : 52,8 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9781482223583
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
Author : Lokenath Debnath
Publisher : CRC Press
Page : 480 pages
File Size : 43,9 Mb
Release : 1995-07-03
Category : Mathematics
ISBN : 0849394589
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.
Author : Virginia S Kiryakova
Publisher : CRC Press
Page : 412 pages
File Size : 53,6 Mb
Release : 1993-12-27
Category : Mathematics
ISBN : 0582219779
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.
Author : Xiao-Jun Yang
Publisher : CRC Press
Page : 306 pages
File Size : 44,9 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9780429811524
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.
Author : Jagdev Singh,Hemen Dutta,Devendra Kumar,Dumitru Baleanu,Jordan Hristov
Publisher : Springer Nature
Page : 433 pages
File Size : 42,7 Mb
Release : 2021-08-26
Category : Technology & Engineering
ISBN : 9783030771690
This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.
Author : Ahmed I. Zayed
Publisher : CRC Press
Page : 280 pages
File Size : 43,6 Mb
Release : 2024-03-28
Category : Mathematics
ISBN : 9781040003664
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.
Author : Carlo Cattani,Hari M. Srivastava,Xiao-Jun Yang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 392 pages
File Size : 41,6 Mb
Release : 2015-01-01
Category : Mathematics
ISBN : 9783110472097
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.
Author : Santanu Saha Ray
Publisher : Springer Nature
Page : 409 pages
File Size : 50,9 Mb
Release : 2019-12-28
Category : Mathematics
ISBN : 9789811516566
This book discusses various novel analytical and numerical methods for solving partial and fractional differential equations. Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by using Euler–Maruyama and strong-order Taylor numerical methods. The book also shows how to arrive at new, exact solutions to various fractional differential equations, such as the time-fractional Burgers–Hopf equation, the (3+1)-dimensional time-fractional Khokhlov–Zabolotskaya–Kuznetsov equation, (3+1)-dimensional time-fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov equation, fractional (2+1)-dimensional Davey–Stewartson equation, and integrable Davey–Stewartson-type equation. Many of the methods discussed are analytical–numerical, namely the modified decomposition method, a new two-step Adomian decomposition method, new approach to the Adomian decomposition method, modified homotopy analysis method with Fourier transform, modified fractional reduced differential transform method (MFRDTM), coupled fractional reduced differential transform method (CFRDTM), optimal homotopy asymptotic method, first integral method, and a solution procedure based on Haar wavelets and the operational matrices with function approximation. The book proposes for the first time a generalized order operational matrix of Haar wavelets, as well as new techniques (MFRDTM and CFRDTM) for solving fractional differential equations. Numerical methods used to solve stochastic point kinetic equations, like the Wiener process, Euler–Maruyama, and order 1.5 strong Taylor methods, are also discussed.
Author : Geeta Arora,Mangey Ram
Publisher : CRC Press
Page : 177 pages
File Size : 44,9 Mb
Release : 2024-01-23
Category : Mathematics
ISBN : 9781003811022
Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems. The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.
Author : Brian Davies
Publisher : Springer Science & Business Media
Page : 398 pages
File Size : 54,9 Mb
Release : 2002-01-02
Category : Mathematics
ISBN : 0387953140
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.
Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 752 pages
File Size : 49,9 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110570632
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Author : Olga Moreira
Publisher : Arcler Press
Page : 0 pages
File Size : 55,6 Mb
Release : 2018-12
Category : Mathematics
ISBN : 1773615548
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.
Author : Artur Babiarz,Adam Czornik,Jerzy Klamka,Michał Niezabitowski
Publisher : Springer
Page : 512 pages
File Size : 42,8 Mb
Release : 2016-09-15
Category : Technology & Engineering
ISBN : 9783319454740
This book collects papers from the 8th Conference on Non-Integer Order Calculus and Its Applications that have been held on September 20-21, 2016 in Zakopane, Poland. The preceding two conferences were held in Szczecin, Poland in 2015, and in Opole, Poland, in 2014. This conference provides a platform for academic exchange on the theory and application of fractional calculus between domestic and international universities, research institutes, corporate experts and scholars. The Proceedings of the 8th Conference on Non-Integer Order Calculus and Its Applications 2016 brings together rigorously reviewed contributions from leading international experts. The included papers cover novel various important aspects of mathematical foundations of fractional calculus, modeling and control of fractional systems as well as controllability, detectability, observability and stability problems for this systems.