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Root Operators and “Evolution” Equations

Author

Listed:
  • Giuseppe Dattoli

    (ENEA UTAPRAD-MAT Laboratorio di Modellistica Matematica, via E. Fermi 45, 00044 Frascati (Rome), Italy)

  • Amalia Torre

    (ENEA UTAPRAD-MAT Laboratorio di Modellistica Matematica, via E. Fermi 45, 00044 Frascati (Rome), Italy)

Abstract

Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained by the Dirac-method as well as results from other methods, specifically in connection with evolution-like equations ruled by square-root operators, that we will address to as relativistic evolution equations.

Suggested Citation

  • Giuseppe Dattoli & Amalia Torre, 2015. "Root Operators and “Evolution” Equations," Mathematics, MDPI, vol. 3(3), pages 1-37, August.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:3:p:690-726:d:54132
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Zine El Abiddine Fellah & Erick Ogam & Mohamed Fellah & Claude Depollier, 2021. "Factorization à la Dirac Applied to Some Equations of Classical Physics," Mathematics, MDPI, vol. 9(8), pages 1-14, April.

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