Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications
Author: Xiao Jun Yang,Dumitru Baleanu,H. M. Srivastava
Publsiher: Academic Press
Total Pages: 262
Release: 2015-10-01
ISBN 10: 9780128040027
ISBN 13: 0128040025
Language: EN, FR, DE, ES & NL

Local Fractional Integral Transforms and Their Applications Book Review:

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

Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications
Author: Xiao Jun Yang,Dumitru Baleanu,H. M. Srivastava
Publsiher: Academic Press
Total Pages: 262
Release: 2015-10-22
ISBN 10: 0128040327
ISBN 13: 9780128040324
Language: EN, FR, DE, ES & NL

Local Fractional Integral Transforms and Their Applications Book Review:

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

General Fractional Derivatives

General Fractional Derivatives
Author: Xiao-Jun Yang
Publsiher: CRC Press
Total Pages: 364
Release: 2019-05-10
ISBN 10: 0429811527
ISBN 13: 9780429811524
Language: EN, FR, DE, ES & NL

General Fractional Derivatives Book Review:

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.

Mathematical Methods in Engineering

Mathematical Methods in Engineering
Author: Kenan Taş,Dumitru Baleanu,J. A. Tenreiro Machado
Publsiher: Springer
Total Pages: 264
Release: 2018-08-02
ISBN 10: 331990972X
ISBN 13: 9783319909721
Language: EN, FR, DE, ES & NL

Mathematical Methods in Engineering Book Review:

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
Author: Santanu Saha Ray
Publsiher: Springer Nature
Total Pages: 388
Release: 2019-12-28
ISBN 10: 9811516561
ISBN 13: 9789811516566
Language: EN, FR, DE, ES & NL

Nonlinear Differential Equations in Physics Book Review:

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.

Basic Theory

Basic Theory
Author: Anatoly Kochubei,Yuri Luchko
Publsiher: Walter de Gruyter GmbH & Co KG
Total Pages: 489
Release: 2019-02-19
ISBN 10: 3110571625
ISBN 13: 9783110571622
Language: EN, FR, DE, ES & NL

Basic Theory Book Review:

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
Author: Artur Babiarz,Adam Czornik,Jerzy Klamka,Michał Niezabitowski
Publsiher: Springer
Total Pages: 512
Release: 2016-09-15
ISBN 10: 3319454749
ISBN 13: 9783319454740
Language: EN, FR, DE, ES & NL

Theory and Applications of Non integer Order Systems Book Review:

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.

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations
Author: Santanu Saha Ray,Arun Kumar Gupta
Publsiher: CRC Press
Total Pages: 273
Release: 2018-01-12
ISBN 10: 1351682210
ISBN 13: 9781351682213
Language: EN, FR, DE, ES & NL

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations Book Review:

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.

Fractional Dynamics

Fractional Dynamics
Author: Carlo Cattani,Hari M. Srivastava,Xiao-Jun Yang
Publsiher: Walter de Gruyter GmbH & Co KG
Total Pages: 392
Release: 2015-01-01
ISBN 10: 3110472090
ISBN 13: 9783110472097
Language: EN, FR, DE, ES & NL

Fractional Dynamics Book Review:

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.

Generalized Fractional Order Differential Equations Arising in Physical Models

Generalized Fractional Order Differential Equations Arising in Physical Models
Author: Santanu Saha Ray,Subhadarshan Sahoo
Publsiher: CRC Press
Total Pages: 314
Release: 2018-11-13
ISBN 10: 0429771789
ISBN 13: 9780429771781
Language: EN, FR, DE, ES & NL

Generalized Fractional Order Differential Equations Arising in Physical Models Book Review:

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.

Frontiers in Fractional Calculus

Frontiers in Fractional Calculus
Author: Sachin Bhalekar
Publsiher: Bentham Science Publishers
Total Pages: 381
Release: 2018-03-21
ISBN 10: 1681085992
ISBN 13: 9781681085999
Language: EN, FR, DE, ES & NL

Frontiers in Fractional Calculus Book Review:

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
Author: Dumitru Baleanu,Devendra Kumar
Publsiher: Frontiers Media SA
Total Pages: 93
Release: 2019-11-15
ISBN 10: 2889459586
ISBN 13: 9782889459582
Language: EN, FR, DE, ES & NL

Fractional Calculus and its Applications in Physics Book Review:

Solved Exercises in Fractional Calculus

Solved Exercises in Fractional Calculus
Author: Edmundo Capelas de Oliveira
Publsiher: Springer
Total Pages: 321
Release: 2019-05-31
ISBN 10: 303020524X
ISBN 13: 9783030205249
Language: EN, FR, DE, ES & NL

Solved Exercises in Fractional Calculus Book Review:

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.

Discontinuity and Complexity in Nonlinear Physical Systems

Discontinuity and Complexity in Nonlinear Physical Systems
Author: J. A. Tenreiro Machado,Dumitru Baleanu,Albert C J Luo
Publsiher: Springer Science & Business Media
Total Pages: 433
Release: 2013-12-04
ISBN 10: 3319014110
ISBN 13: 9783319014111
Language: EN, FR, DE, ES & NL

Discontinuity and Complexity in Nonlinear Physical Systems Book Review:

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.

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

New Trends in Fractional Differential Equations with Real World Applications in Physics
Author: Jagdev Singh,Jordan Yankov Hristov,Zakia Hammouch
Publsiher: Frontiers Media SA
Total Pages: 329
Release: 2020-12-30
ISBN 10: 2889663043
ISBN 13: 9782889663040
Language: EN, FR, DE, ES & NL

New Trends in Fractional Differential Equations with Real World Applications in Physics Book Review:

Mathematical Modeling using Differential Equations and Network Theory

Mathematical Modeling using Differential Equations  and Network Theory
Author: Ioannis Dassios
Publsiher: MDPI
Total Pages: 160
Release: 2020-06-23
ISBN 10: 3039288253
ISBN 13: 9783039288250
Language: EN, FR, DE, ES & NL

Mathematical Modeling using Differential Equations and Network Theory Book Review:

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.

The Craft of Fractional Modelling in Science and Engineering

The Craft of Fractional Modelling in Science and Engineering
Author: Jordan Hristov
Publsiher: MDPI
Total Pages: 138
Release: 2018-06-22
ISBN 10: 303842983X
ISBN 13: 9783038429838
Language: EN, FR, DE, ES & NL

The Craft of Fractional Modelling in Science and Engineering Book Review:

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

Mathematical Analysis and Applications

Mathematical Analysis and Applications
Author: Hari Mohan Srivastava
Publsiher: MDPI
Total Pages: 220
Release: 2019-01-14
ISBN 10: 3038974005
ISBN 13: 9783038974000
Language: EN, FR, DE, ES & NL

Mathematical Analysis and Applications Book Review:

This book is a printed edition of the Special Issue "Mathematical Analysis and Applications" that was published in Axioms

Fractional Derivatives with Mittag Leffler Kernel

Fractional Derivatives with Mittag Leffler Kernel
Author: José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Publsiher: Springer
Total Pages: 341
Release: 2019-02-13
ISBN 10: 303011662X
ISBN 13: 9783030116620
Language: EN, FR, DE, ES & NL

Fractional Derivatives with Mittag Leffler Kernel Book Review:

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.

Integral Transforms and their Applications

Integral Transforms and their Applications
Author: B. Davies
Publsiher: Springer Science & Business Media
Total Pages: 419
Release: 2013-11-11
ISBN 10: 1489926917
ISBN 13: 9781489926913
Language: EN, FR, DE, ES & NL

Integral Transforms and their Applications Book Review:

In preparing this second edition I have restricted myself to making small corrections and changes to the first edition. Two chapters have had extensive changes made. First, the material of Sections 14.1 and 14.2 has been rewritten to make explicit reference to the book of Bleistein and Handelsman, which appeared after the original Chapter 14 had been written. Second, Chapter 21, on numerical methods, has been rewritten to take account of comparative work which was done by the author and Brian Martin, and published as a review paper. The material for all of these chapters was in fact, prepared for a transla tion of the book. Considerable thought has been given to a much more com prehensive revision and expansion of the book. In particular, there have been spectacular advances in the solution of some non-linear problems using isospectra1 methods, which may be re garded as a generalization of the Fourier transform. However, the subject is a large one, and even a modest introduction would have added substantially to the book. Moreover, the recent book by Dodd et al. is at a similar level to the present volume. Similarly, I have refrained from expanding the chapter on num erical methods into a complete new part of the book, since a specialized monograph on numerical methods is in preparation in collaboration with a colleague.