Fractional order calculus: historical apologia, basic concepts and some applications

Author:

David S.A.1,Linares J.L.1,Pallone E.M.J.A.1

Affiliation:

1. Universidade de São Paulo, Brasil

Abstract

Fractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. However, until recently, it has been investigated mainly from a mathematical point of view. Advances in the field of fractals have revealed its subtle relationships with fractional calculus. Nonetheless, fractional calculus is generally excluded from standard courses in mathematics, partly because many mathematicians are unfamiliar with its nature and its applications. This area has emerged as a useful tool among researchers. One of the objectives of this paper is to discuss the usefulness of fractional calculus in applied sciences and engineering. In view of the increasing interest in the development of the new paradigm, another objective is to encourage the use of this mathematical idea in various scientific areas by means of a historical apologia for the development of fractional calculus.

Publisher

FapUNIFESP (SciELO)

Subject

General Physics and Astronomy,Education

Reference29 articles.

1. Fractional relaxation-oscillation and fractional diffusion-wave phenomena

2. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order;Oldham K.B.,2006

3. On the Fractional Calculus Model of Viscoelastic Behavior

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