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Fractional calculus and fractional order operators

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Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

Part of the book series: Developments in Mathematics ((DEVM,volume 41))

Abstract

Fractional order differential equations are an efficient tool to model various processes arising in science and engineering. Fractional models adequately reflect subtle internal properties, such as memory or hereditary properties, of complex processes that the classical integer order models neglect. In this chapter we will discuss the theoretical background of fractional modeling, that is the fractional calculus, including recent developments - distributed and variable fractional order differential operators.

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Notes

  1. 1.

    The first existing documented record on fractional derivatives goes back to year 1695. Leibniz in his letter (dated September 30, 1695) to L’Hôpital wrote on the derivative of order 1/2 of the function f(t) = t.

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Authors and Affiliations

  1. Department of Mathematics, University of New Haven, West Haven, CT, USA

    Sabir Umarov

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  1. Sabir Umarov
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Umarov, S. (2015). Fractional calculus and fractional order operators. In: Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Developments in Mathematics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-20771-1_3

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