Fractional Integrals And Derivatives PDF Download
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Author | : Stefan Samko |
Publisher | : CRC Press |
Total Pages | : 1016 |
Release | : 1993-12-08 |
Genre | : Mathematics |
ISBN | : 9782881248641 |
Download Fractional Integrals and Derivatives Book in PDF, ePub and Kindle
In San Francisco, a fisherman's get-rich-quick scheme ends in violence. As sharks fetch high prices, he hires a professional shark hunter to go fishing, the deal being he gets the first three tons, the hunter the rest. But as the hunter's share piles up, jealousy rears its head.
Author | : Changpin Li |
Publisher | : SIAM |
Total Pages | : 326 |
Release | : 2019-10-31 |
Genre | : Mathematics |
ISBN | : 1611975883 |
Download Theory and Numerical Approximations of Fractional Integrals and Derivatives Book in PDF, ePub and Kindle
Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus, provides a detailed treatment of existing numerical approximations, and presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.
Author | : Yuri Luchko |
Publisher | : MDPI |
Total Pages | : 280 |
Release | : 2021-03-16 |
Genre | : Mathematics |
ISBN | : 303650494X |
Download Fractional Integrals and Derivatives: “True” versus “False” Book in PDF, ePub and Kindle
This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.
Author | : Xiao-Jun Yang |
Publisher | : CRC Press |
Total Pages | : 306 |
Release | : 2019-05-10 |
Genre | : Mathematics |
ISBN | : 0429811527 |
Download General Fractional Derivatives Book in PDF, ePub and Kindle
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.
Author | : Rudolf Hilfer |
Publisher | : World Scientific |
Total Pages | : 473 |
Release | : 2000-03-02 |
Genre | : Science |
ISBN | : 9814496200 |
Download Applications Of Fractional Calculus In Physics Book in PDF, ePub and Kindle
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.
Author | : A.A. Kilbas |
Publisher | : Elsevier |
Total Pages | : 550 |
Release | : 2006-02-16 |
Genre | : Mathematics |
ISBN | : 9780444518323 |
Download Theory and Applications of Fractional Differential Equations Book in PDF, ePub and Kindle
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.
Author | : Igor Podlubny |
Publisher | : Elsevier |
Total Pages | : 366 |
Release | : 1998-10-27 |
Genre | : Mathematics |
ISBN | : 0080531989 |
Download Fractional Differential Equations Book in PDF, ePub and Kindle
This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Author | : Saïd Abbas |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 362 |
Release | : 2018-02-05 |
Genre | : Mathematics |
ISBN | : 3110553813 |
Download Implicit Fractional Differential and Integral Equations Book in PDF, ePub and Kindle
This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations
Author | : Anatoly A. Kilbas |
Publisher | : CRC Press |
Total Pages | : 399 |
Release | : 2004-03-17 |
Genre | : Mathematics |
ISBN | : 0203487370 |
Download H-Transforms Book in PDF, ePub and Kindle
Along with more than 2100 integral equations and their solutions, this handbook outlines exact analytical methods for solving linear and nonlinear integral equations and provides an evaluation of approximate methods. Each section provides examples that show how methods can be applied to specific equations.
Author | : J. Sabatier |
Publisher | : Springer Science & Business Media |
Total Pages | : 550 |
Release | : 2007-07-28 |
Genre | : Technology & Engineering |
ISBN | : 1402060424 |
Download Advances in Fractional Calculus Book in PDF, ePub and Kindle
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.