Initialization, conceptualization, and application in the generalized fractional calculus

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Published **1998**
by National Aeronautics and Space Administration, Lewis Research Center, Available from NASA Center for Aerospace Information in Cleveland, Ohio, Hanover, Md .

Written in English

- Fractional calculus.

**Edition Notes**

Statement | Carl F. Lorenzo, Tom T. Hartley. |

Series | NASA technical paper -- 1998-208415 |

Contributions | Hartley, T. T. 1964-, Lewis Research Center. |

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

Pagination | v, 107 p. : |

Number of Pages | 107 |

ID Numbers | |

Open Library | OL20705355M |

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to. Special issue: Initialization, conceptualization, and application in the generalized fractional calculus. Lorenzo CF(1), Hartley TT. Author information: (1)NASA Glenn Research Center, National Aeronautics and Space Administration, Brookpark Road, Cleveland, Ohio, by: 3. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus. By Carl F. Lorenzo and Tom T. Hartley. Abstract. This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to Author: Carl F. Lorenzo and Tom T. Hartley.

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral : Virginia S Kiryakova. The fractional calculus is widely popular, especially in the field of viscoelasticity. In this chapter variety of applications are discussed. This chapter is application oriented to demonstrate the fundamental of generalized (fractional) calculus developed earlier, with particular reference to initialization concepts. Buy Initialization, conceptualization, and application in the generalized fractional calculus (NASA technical paper) by Carl F Lorenzo (ISBN:) from Amazon's Book Store. Everyday low prices and free delivery on eligible : Carl F Lorenzo. Fractional calculus is a ﬁeld of mathematics study that qrows out of the tra-ditional deﬁnitions of calculus integral and derivative operators in much the sameway fractionalexponentsis anoutgrowthof exponentswithintegervalue. The concept of fractional calculus(fractional derivatives and fractional in-tegral) is not new.

The next three Chapters (5, 6, 7) are related to applications of fractional calculus in bio-engineering fields. Chapter 5 is dedicated to the mathematical modeling of skin structure applying fractional calculus where it is proposed the skin structure as a more complex system . It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized fractional integral and derivative that generalize those for the integer-order by: Key words and phrases. Fractional Calculus, Generalized fractional derivatives, Riemann-Liouville fractional derivative, Hadamard fractional derivative, Erd´elyi-Kober operator, Taylor series expansion. c Universiteti i Prishtin¨es, Prishtin¨e, Kosov¨e. Submitted December 2, Published Octo Email:[email protected] 1. Part 1 of this book presents an introduction to fractional calculus. Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives. Part 2 is the central part of the book.

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