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Local Fractional Integral Transforms And Their Applications

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Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications Book
Author : Xiao Jun Yang,Dumitru Baleanu,H. M. Srivastava
Publisher : Academic Press
Release : 2015-10-22
ISBN : 0128040327
Language : En, Es, Fr & De

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Book Description :

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

Methods of Mathematical Modelling and Computation for Complex Systems

Methods of Mathematical Modelling and Computation for Complex Systems Book
Author : Jagdev Singh,Hemen Dutta,Devendra Kumar,Dumitru Baleanu,Jordan Hristov
Publisher : Springer Nature
Release : 2021-08-26
ISBN : 3030771695
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical Methods in Engineering

Mathematical Methods in Engineering Book
Author : Kenan Taş,Dumitru Baleanu,J. A. Tenreiro Machado
Publisher : Springer
Release : 2018-08-02
ISBN : 331990972X
Language : En, Es, Fr & De

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Book Description :

This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.

Nonlinear Differential Equations in Physics

Nonlinear Differential Equations in Physics Book
Author : Santanu Saha Ray
Publisher : Springer Nature
Release : 2019-12-28
ISBN : 9811516561
Language : En, Es, Fr & De

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Book Description :

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.

Fractional Dynamics

Fractional Dynamics Book
Author : Carlo Cattani,Hari M. Srivastava,Xiao-Jun Yang
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2015-01-01
ISBN : 3110472090
Language : En, Es, Fr & De

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Book Description :

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.

Basic Theory

Basic Theory Book
Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2019-02-19
ISBN : 3110570637
Language : En, Es, Fr & De

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Book Description :

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.

Theory and Applications of Non integer Order Systems

Theory and Applications of Non integer Order Systems Book
Author : Artur Babiarz,Adam Czornik,Jerzy Klamka,Michał Niezabitowski
Publisher : Springer
Release : 2016-09-15
ISBN : 3319454749
Language : En, Es, Fr & De

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Book Description :

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.

Frontiers in Fractional Calculus

Frontiers in Fractional Calculus Book
Author : Sachin Bhalekar
Publisher : Bentham Science Publishers
Release : 2018-03-21
ISBN : 1681085992
Language : En, Es, Fr & De

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Book Description :

This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.

Fractional Calculus and its Applications in Physics

Fractional Calculus and its Applications in Physics Book
Author : Dumitru Baleanu,Devendra Kumar
Publisher : Frontiers Media SA
Release : 2019-11-15
ISBN : 2889459586
Language : En, Es, Fr & De

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Book Description :

Download Fractional Calculus and its Applications in Physics book written by Dumitru Baleanu,Devendra Kumar, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Solved Exercises in Fractional Calculus

Solved Exercises in Fractional Calculus Book
Author : Edmundo Capelas de Oliveira
Publisher : Springer
Release : 2019-05-31
ISBN : 303020524X
Language : En, Es, Fr & De

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Book Description :

This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations Book
Author : Santanu Saha Ray,Arun Kumar Gupta
Publisher : CRC Press
Release : 2018-01-12
ISBN : 1351682210
Language : En, Es, Fr & De

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Book Description :

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.

Generalized Fractional Order Differential Equations Arising in Physical Models

Generalized Fractional Order Differential Equations Arising in Physical Models Book
Author : Santanu Saha Ray,Subhadarshan Sahoo
Publisher : CRC Press
Release : 2018-11-13
ISBN : 0429771789
Language : En, Es, Fr & De

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Book Description :

This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.

Mathematical Modeling using Differential Equations and Network Theory

Mathematical Modeling using Differential Equations  and Network Theory Book
Author : Ioannis Dassios
Publisher : MDPI
Release : 2020-06-23
ISBN : 3039288253
Language : En, Es, Fr & De

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Book Description :

This Special Issue collects the latest results on differential/difference equations, the mathematics of networks, and their applications to engineering and physical phenomena. It features nine high-quality papers that were published with original research results. The Special Issue brings together mathematicians with physicists, engineers, as well as other scientists.

General Fractional Derivatives

General Fractional Derivatives Book
Author : Xiao-Jun Yang
Publisher : CRC Press
Release : 2019-05-10
ISBN : 0429811527
Language : En, Es, Fr & De

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Book Description :

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.

Analysis of Infectious Disease Problems Covid 19 and Their Global Impact

Analysis of Infectious Disease Problems  Covid 19  and Their Global Impact Book
Author : Praveen Agarwal,Juan J. Nieto,Michael Ruzhansky,Delfim F. M. Torres
Publisher : Springer Nature
Release : 2021
ISBN : 981162450X
Language : En, Es, Fr & De

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Book Description :

This edited volume is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. Divided into two parts, the book gives a general and country-wise analysis of Covid-19. Analytical and numerical techniques for virus models are presented along with the application of mathematical modelling in the analysis of their spreading rates and treatments. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods. Probability distribution and their bio-mathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.

Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems

Multi Chaos  Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems Book
Author : Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis
Publisher : Academic Press
Release : 2022-07-01
ISBN : 0323886167
Language : En, Es, Fr & De

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Book Description :

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.

New Trends in Fractional Differential Equations with Real World Applications in Physics

New Trends in Fractional Differential Equations with Real World Applications in Physics Book
Author : Jagdev Singh,Jordan Yankov Hristov,Zakia Hammouch
Publisher : Frontiers Media SA
Release : 2020-12-30
ISBN : 2889663043
Language : En, Es, Fr & De

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Book Description :

This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.

The Craft of Fractional Modelling in Science and Engineering

The Craft of Fractional Modelling in Science and Engineering Book
Author : Jordan Hristov
Publisher : MDPI
Release : 2018-06-22
ISBN : 303842983X
Language : En, Es, Fr & De

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Book Description :

This book is a printed edition of the Special Issue "The Craft of Fractional Modelling in Science and Engineering" that was published in Fractal Fract

Discontinuity and Complexity in Nonlinear Physical Systems

Discontinuity and Complexity in Nonlinear Physical Systems Book
Author : J. A. Tenreiro Machado,Dumitru Baleanu,Albert C J Luo
Publisher : Springer Science & Business Media
Release : 2013-12-04
ISBN : 3319014110
Language : En, Es, Fr & De

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Book Description :

Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.

Integral Transforms and Their Applications

Integral Transforms and Their Applications Book
Author : Lokenath Debnath,Dambaru Bhatta
Publisher : CRC Press
Release : 2014-11-07
ISBN : 1482223589
Language : En, Es, Fr & De

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Book Description :

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