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Root Operators and “Evolution” Equations

ENEA UTAPRAD-MAT Laboratorio di Modellistica Matematica, via E. Fermi 45, 00044 Frascati (Rome), Italy
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Mathematics 2015, 3(3), 690-726;
Received: 19 January 2015 / Revised: 14 July 2015 / Accepted: 28 July 2015 / Published: 13 August 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
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. View Full-Text
Keywords: dirac equation; evolution equation; root operator dirac equation; evolution equation; root operator
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MDPI and ACS Style

Dattoli, G.; Torre, A. Root Operators and “Evolution” Equations. Mathematics 2015, 3, 690-726.

AMA Style

Dattoli G, Torre A. Root Operators and “Evolution” Equations. Mathematics. 2015; 3(3):690-726.

Chicago/Turabian Style

Dattoli, Giuseppe, and Amalia Torre. 2015. "Root Operators and “Evolution” Equations" Mathematics 3, no. 3: 690-726.

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