Next Article in Journal
From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity
Next Article in Special Issue
A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus
Previous Article in Journal
Evaluation of Interpolants in Their Ability to Fit Seismometric Time Series
Previous Article in Special Issue
Time Automorphisms on C*-Algebras
Article Menu

Export Article

Open AccessArticle
Mathematics 2015, 3(3), 690-726; doi:10.3390/math3030690

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
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)
View Full-Text   |   Download PDF [545 KB, uploaded 13 August 2015]   |  

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. View Full-Text
Keywords: dirac equation; evolution equation; root operator dirac equation; evolution equation; root operator
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top