## Local Fractional Integral Transforms and Their Applications

• Author : Xiao Jun Yang
• Release Date : 2015-10-22
• Genre: Mathematics
• Pages : 262
• ISBN 10 : 9780128040324

Local Fractional Integral Transforms and Their Applications Excerpt :

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

• Author : Xiao Jun Yang
• Release Date : 2015-10-01
• Genre: Uncategoriezed
• Pages : 262
• ISBN 10 : 0128040025

Local Fractional Integral Transforms and Their Applications Excerpt :

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

## Mathematical Methods in Engineering

• Author : Kenan Taş
• Publisher : Springer
• Release Date : 2018-08-02
• Genre: Technology & Engineering
• Pages : 264
• ISBN 10 : 9783319909721

Mathematical Methods in Engineering Excerpt :

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.

## Methods of Mathematical Modelling and Computation for Complex Systems

• Author : Jagdev Singh
• Publisher : Springer Nature
• Release Date : 2021-08-26
• Genre: Technology & Engineering
• Pages : 433
• ISBN 10 : 9783030771690

Methods of Mathematical Modelling and Computation for Complex Systems Excerpt :

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.

## Nonlinear Differential Equations in Physics

• Author : Santanu Saha Ray
• Publisher : Springer Nature
• Release Date : 2019-12-28
• Genre: Mathematics
• Pages : 388
• ISBN 10 : 9789811516566

Nonlinear Differential Equations in Physics Excerpt :

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

• Author : Anatoly Kochubei
• Publisher : Walter de Gruyter GmbH & Co KG
• Release Date : 2019-02-19
• Genre: Mathematics
• Pages : 489
• ISBN 10 : 9783110570632

Basic Theory Excerpt :

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

• Author : Artur Babiarz
• Publisher : Springer
• Release Date : 2016-09-15
• Genre: Technology & Engineering
• Pages : 512
• ISBN 10 : 9783319454740

Theory and Applications of Non integer Order Systems Excerpt :

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

• Author : Sachin Bhalekar
• Publisher : Bentham Science Publishers
• Release Date : 2018-03-21
• Genre: Mathematics
• Pages : 381
• ISBN 10 : 9781681085999

Frontiers in Fractional Calculus Excerpt :

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

• Author : Dumitru Baleanu
• Publisher : Frontiers Media SA
• Release Date : 2019-11-15
• Genre: Uncategoriezed
• Pages : 93
• ISBN 10 : 9782889459582

Fractional Calculus and its Applications in Physics Excerpt :

## Solved Exercises in Fractional Calculus

• Author : Edmundo Capelas de Oliveira
• Publisher : Springer
• Release Date : 2019-05-31
• Genre: Technology & Engineering
• Pages : 321
• ISBN 10 : 9783030205249

Solved Exercises in Fractional Calculus Excerpt :

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

• Author : Santanu Saha Ray
• Publisher : CRC Press
• Release Date : 2018-01-12
• Genre: Mathematics
• Pages : 273
• ISBN 10 : 9781351682213

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations Excerpt :

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

• Author : Santanu Saha Ray
• Publisher : CRC Press
• Release Date : 2018-11-13
• Genre: Mathematics
• Pages : 314
• ISBN 10 : 9780429771781

Generalized Fractional Order Differential Equations Arising in Physical Models Excerpt :

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.

## Fractional Dynamics

• Author : Carlo Cattani
• Publisher : Walter de Gruyter GmbH & Co KG
• Release Date : 2015-01-01
• Genre: Mathematics
• Pages : 392
• ISBN 10 : 9783110472097

Fractional Dynamics Excerpt :

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.

## Mathematical Modeling using Differential Equations and Network Theory

• Author : Ioannis Dassios
• Publisher : MDPI
• Release Date : 2020-06-23
• Genre: Technology & Engineering
• Pages : 160
• ISBN 10 : 9783039288250

Mathematical Modeling using Differential Equations and Network Theory Excerpt :

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

• Author : Xiao-Jun Yang
• Publisher : CRC Press
• Release Date : 2019-05-10
• Genre: Mathematics
• Pages : 364
• ISBN 10 : 9780429811524

General Fractional Derivatives Excerpt :

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.