Fractional Calculus Integral and Differential Equations of Fractional Order by Rudolf Gorenflo, Francesco Mainardi

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About this book :-
Fractional Calculus Integral and Differential Equations of Fractional Order written by Rudolf Gorenflo, Francesco Mainardi.
In these lectures the author introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating these operators in a way accessible to applied scientists, avoiding unproductive generalities and excessive mathematical rigor. By applying this technique the author derived the analytical solutions of the most simple linear integral and differential equations of fractional order.
It also show the fundamental role of the Mittag-Leffler function, whose properties are reported in an ad hoc Appendix. The topics discussed here are : (a) essentials of Riemann-Liouville fractional calculus with basic formulas of Laplace transforms, (b) Abel type integral equations of first and second kind, (c) relaxation and oscillation type differential equations of fractional order.

Book Detail :-
Title: Fractional Calculus Integral and Differential Equations of Fractional Order
Edition:
Author(s): Rudolf Gorenflo, Francesco Mainardi
Publisher:
Series:
Year: 2000
Pages: 56
Type: PDF
Language: English
ISBN: 3-211-82913-X
Country: Germany
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Book Contents :-
Fractional Calculus Integral and Differential Equations of Fractional Order written by Rudolf Gorenflo, Francesco Mainardi cover the following topics.
Abstract
1. Introduction to fractional calculus
2. Fractional Integral Equations
3. Fractional Differential Equations 1
4. Fractional Differential Equations 2
Conclustions
Appendix: The Mittag Leffler Type Functions
Refrences

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