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A Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients

Author

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  • Francesco Mainardi

    (Department of Physics and Astronomy, University of Bologna, and the National Institute of Nuclear Physics (INFN), Via Irnerio, 46, I-40126 Bologna, Italy)

Abstract

In this note, we show how an initial value problem for a relaxation process governed by a differential equation of a non-integer order with a constant coefficient may be equivalent to that of a differential equation of the first order with a varying coefficient. This equivalence is shown for the simple fractional relaxation equation that points out the relevance of the Mittag–Leffler function in fractional calculus. This simple argument may lead to the equivalence of more general processes governed by evolution equations of fractional order with constant coefficients to processes governed by differential equations of integer order but with varying coefficients. Our main motivation is to solicit the researchers to extend this approach to other areas of applied science in order to have a deeper knowledge of certain phenomena, both deterministic and stochastic ones, investigated nowadays with the techniques of the fractional calculus.

Suggested Citation

  • Francesco Mainardi, 2018. "A Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients," Mathematics, MDPI, vol. 6(1), pages 1-5, January.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:1:p:8-:d:126113
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    Cited by:

    1. Sania Qureshi & Norodin A. Rangaig & Dumitru Baleanu, 2019. "New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator," Mathematics, MDPI, vol. 7(4), pages 1-14, April.

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