Fractional Calculus in Bioengineering

Fractional Calculus in Bioengineering
Author :
Publisher :
Total Pages :
Release :
ISBN-10 : 1567004954
ISBN-13 : 9781567004953
Rating : 4/5 (54 Downloads)

Synopsis Fractional Calculus in Bioengineering by : Richard L. Magin

"This book is written for bioengineers who wish to learn more about fractional calculus (integration and differentiation of arbitrary order) and the ways in which it can be used to solve biomedical problems. However, the text covers a wide range of topics (bioelectrodes, biomaterials, neural networks, etc.) that I hope will be of interest to other scientists and engineers as well as to bioengineers. Examples and exercises show that with only a small change in notation and perspective, fractional calculus extends many of the modeling capabilities of conventional calculus and integer order differential equations. By combining an "engineer's" approach to fractional calculus - largely through using the Laplace transform - with examples taken from a variety of biomedical applications, this book will help new students learn to use the techniques of fractional calculus. The second edition of this book contains updates and corrections to equations and descriptions from the first edition"--

Fractional Calculus and Waves in Linear Viscoelasticity

Fractional Calculus and Waves in Linear Viscoelasticity
Author :
Publisher : World Scientific
Total Pages : 368
Release :
ISBN-10 : 9781848163300
ISBN-13 : 1848163304
Rating : 4/5 (00 Downloads)

Synopsis Fractional Calculus and Waves in Linear Viscoelasticity by : Francesco Mainardi

This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types. It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography. This book is likely to be of interest to applied scientists and engineers.

Fractional Calculus with its Applications in Engineering and Technology

Fractional Calculus with its Applications in Engineering and Technology
Author :
Publisher : Springer Nature
Total Pages : 95
Release :
ISBN-10 : 9783031796258
ISBN-13 : 303179625X
Rating : 4/5 (58 Downloads)

Synopsis Fractional Calculus with its Applications in Engineering and Technology by : Yi Yang

This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grünwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).

Advances in Fractional Calculus

Advances in Fractional Calculus
Author :
Publisher : Springer Science & Business Media
Total Pages : 550
Release :
ISBN-10 : 9781402060427
ISBN-13 : 1402060424
Rating : 4/5 (27 Downloads)

Synopsis Advances in Fractional Calculus by : J. Sabatier

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Fractional Calculus in Bioengineering

Fractional Calculus in Bioengineering
Author :
Publisher :
Total Pages : 684
Release :
ISBN-10 : 1567002153
ISBN-13 : 9781567002157
Rating : 4/5 (53 Downloads)

Synopsis Fractional Calculus in Bioengineering by : Richard L. Magin

Fractional Calculus and Fractional Differential Equations

Fractional Calculus and Fractional Differential Equations
Author :
Publisher : Springer
Total Pages : 187
Release :
ISBN-10 : 9789811392276
ISBN-13 : 9811392277
Rating : 4/5 (76 Downloads)

Synopsis Fractional Calculus and Fractional Differential Equations by : Varsha Daftardar-Gejji

This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.

Discrete Fractional Calculus: Applications In Control And Image Processing

Discrete Fractional Calculus: Applications In Control And Image Processing
Author :
Publisher : World Scientific
Total Pages : 396
Release :
ISBN-10 : 9789814725682
ISBN-13 : 9814725684
Rating : 4/5 (82 Downloads)

Synopsis Discrete Fractional Calculus: Applications In Control And Image Processing by : Piotr Ostalczyk

The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.

The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations
Author :
Publisher : Springer
Total Pages : 251
Release :
ISBN-10 : 9783642145742
ISBN-13 : 3642145744
Rating : 4/5 (42 Downloads)

Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Fractional Calculus for Skeptics I

Fractional Calculus for Skeptics I
Author :
Publisher : CRC Press
Total Pages : 147
Release :
ISBN-10 : 9781040012697
ISBN-13 : 1040012698
Rating : 4/5 (97 Downloads)

Synopsis Fractional Calculus for Skeptics I by : Bruce J. West

This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.