5 edition of **Fractional Calculus and Its Applications** found in the catalog.

Fractional Calculus and Its Applications

Bertram Ross

- 341 Want to read
- 39 Currently reading

Published
**June 1974** by Springer-Verlag .

Written in English

The Physical Object | |
---|---|

Number of Pages | 381 |

ID Numbers | |

Open Library | OL7442502M |

ISBN 10 | 038707161X |

ISBN 10 | 9780387071619 |

Many special cases, including cosine and sine function, are also discussed by the authors and some profound consequences have been drawn. The existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations is studied with -Laplacian operator. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. Analogously all the functions curves with the same critical order and the same will form an equivalence class modeled by If f differs from by a logarithmic correction then terms on the RHS of equation do not make sense like in the ordinary calculus. These methods can be applied in finance, to model tick-by-tick log -price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.

Monje has been working on fractional derivatives and their applications for over seven years being author and co-author of over 40 technical papers mostly related to fractional-order controllers. The proposed method is based on the minimization of the integral of square error ISE between the step responses of a unit feedback control system, whose open-loop transfer function is given by a fractional-order integrator and that of the PID compensated system [ 7 ]. He primarily teaches the subjects like real and complex analysis, functional analysis, Abstract Algebra and measure theory in post-graduate level course in mathematics. In addition, most physical phenomena of fluid dynamics, quantum mechanics, electricity, ecological systems, and many other models are controlled within their domain of validity by fractional order PDEs. She has co-chaired international conferences and she has been a member of international program committees.

He has also hold some leading jobs in the Spanish National Research Agency. The state observer of fractional dynamical system is presented, and an adaptive pinning controller is designed for a little part of agents in multiagent systems without disturbances. However, later that year, fairly satisfactory answers were given to this question [ 142229 ]. By applying the stability theory of fractional order dynamical systems, the distributed coordination of fractional multiagent systems with external disturbances can be reached asymptotically. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. He is member of Editorial Board of various Journals of Mathematics.

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In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. The papers for this special issue were selected after a careful and studious peer-review process.

Download eBook The Fractional Calculus and Its Applications book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences.

Fractional Riccati Differential Equations. He has also hold some leading jobs in the Spanish National Research Agency. Although, there were various discussions on this issue, the problem was not solved until And the quasi-synchronization error bound can be controlled by choosing the suitable control parameters.

Analogously all the functions curves with the same critical order and the same will form an equivalence class modeled by If f differs from Fractional Calculus and Its Applications book a logarithmic correction then terms on the RHS of equation do not make sense like in the ordinary calculus.

He was on the Thompson Reuter list of high cited researchers inand and Dumitru is a member of the advisory board of the ''Mathematical Methods and Modeling for Complex Phenomena'' book collection, published jointly by Higher Education Press and Springer.

Tsinghua University Press. Moreover, the sufficient condition of the robust synchronization between such neural systems with the same parameter uncertainties is proposed owing to the robust stability analysis of its synchronization error system.

All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics.

Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions. The proposed method is based on the minimization of the integral of square error ISE between the step responses of a unit feedback control system, whose open-loop transfer function is given by a fractional-order integrator and that of the PID compensated system [ 7 ].

Eventually, it may be expected that the present special issue would certainly helpful to explore the researchers with their new arising fractional order problems and elevate the efficiency and accuracy of the solution methods for those problems in use nowadays.

Part III consists of contributions dealing with some problems in applied analysis. The open-loop transfer function is defined as.

Analytical and numerical methods with advanced mathematical modelling and recent developments of differential and integral equations of arbitrary order arising in physical systems are included in the main focus of the issue. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management.

In this Fractional Calculus and Its Applications book, we study a Fractional Calculus and Its Applications book for tuning PID controllers such that the response of the compensated system has an almost constant overshoot defined by a prescribed value.

Figure 1 illustrates the fractional-order control system that will be used as reference model for the tuning of PID controllers. Dumitru's research interests include fractional dynamics and its applications, fractional differential equations, dynamic systems on time scales, Hamilton-Jacobi formalism, Lie symmetries.

He is currently involved as Principal Investigator in research projects with the objective of applying FOC to industrial processes, servomechanisms, and autonomous vehicles, and his current interest in the field also includes stability theory, optimal and adaptive control, and implementation issues using FOC.

Fractional Fornberg-Whitham Equation. The final prices may differ from the prices shown due to specifics of VAT rules About this book Fractional-order Systems and Controls details the use of fractional calculus calculus of non-integer order in the description and modeling of systems, and in a range of control design and practical applications.

The evaluations show that the homotopy decomposition method is extremely successful and suitable. Numerical code is also provided.Fractional calculus is a branch of classical mathematics, which deals with the generalization of operations of differentiation and integration to fractional order.

Such a generalization is not merely a mathematical curiosity but has found applications in various fields of physical sciences. In this paper, we review the definitions and properties of fractional derivatives and integrals, and we.

Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications.

It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical andBrand: Springer-Verlag London. Get this from a library! Fractional calculus and its applications: proceedings of the international conference held at the University of New Haven, June, [Bertram Ross;].In order to READ Online or Download Fractional Calculus Pdf Its Applications pdf in PDF, ePUB, Tuebl and Mobi format, you need to create a FREE account.

We cannot guarantee that Fractional Calculus And Its Applications book is in the library, But if You are still not sure with the service, you can choose FREE Trial service.Fractional calculus is a branch of classical mathematics, which deals with the generalization download pdf operations of differentiation and integration to fractional order.

Such a generalization is not merely a mathematical curiosity but has found applications in various fields of physical sciences. In this paper, we review the definitions and properties of fractional derivatives and integrals, and we.This is the brief version of Calculus ebook Its Applications, Thirteenth Edition, containing chapters 1—9.

Calculus and Its Applications, Thirteenth Edition is a comprehensive, yet flexible, text for students majoring in business, economics, life science, or social sciences.