# General Fractional Derivatives

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### General Fractional Derivatives

Author | : Xiao-Jun Yang |

Publsiher | : CRC Press |

Total Pages | : 306 |

Release | : 2019-05-10 |

Genre | : Mathematics |

ISBN | : 9780429811524 |

**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.

### General Fractional Derivatives with Applications in Viscoelasticity

Author | : Xiao-Jun Yang,Feng Gao,Yang Ju |

Publsiher | : Academic Press |

Total Pages | : 456 |

Release | : 2020-04-03 |

Genre | : Mathematics |

ISBN | : 9780128172094 |

**Download General Fractional Derivatives with Applications in Viscoelasticity Book in PDF, Epub and Kindle**

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus. Presents a comprehensive overview of the fractional derivatives and their applications in viscoelasticity Provides help in handling the power-law functions Introduces and explores the questions about general fractional derivatives and its applications

### Fractional Differential Equations

Author | : Anatoly Kochubei,Yuri Luchko |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 528 |

Release | : 2019-02-19 |

Genre | : Mathematics |

ISBN | : 9783110571660 |

**Download Fractional Differential Equations Book in PDF, Epub and Kindle**

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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

### General Fractional Derivatives

Author | : Xiao-Jun Yang |

Publsiher | : CRC Press |

Total Pages | : 306 |

Release | : 2019-05-10 |

Genre | : Mathematics |

ISBN | : 9780429811524 |

**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.

### Fractional Integrals and Derivatives

Author | : Yuri Luchko |

Publsiher | : Mdpi AG |

Total Pages | : 0 |

Release | : 2021-02-16 |

Genre | : Computers |

ISBN | : 3036504958 |

**Download Fractional Integrals and Derivatives 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.

### Basic Theory

Author | : Anatoly Kochubei,Yuri Luchko |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 752 |

Release | : 2019-02-19 |

Genre | : Mathematics |

ISBN | : 9783110570632 |

**Download Basic Theory Book in PDF, Epub and Kindle**

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.

### Fractional Differential Equations

Author | : Igor Podlubny |

Publsiher | : Elsevier |

Total Pages | : 366 |

Release | : 1998-10-27 |

Genre | : Mathematics |

ISBN | : 9780080531984 |

**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

### Applications Of Fractional Calculus In Physics

Author | : Rudolf Hilfer |

Publsiher | : World Scientific |

Total Pages | : 473 |

Release | : 2000-03-02 |

Genre | : Science |

ISBN | : 9789814496209 |

**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.