Duarte Ortigueira, M. (2006) Riesz Potential Operators and Inverses via Fractional Centred Derivatives. International Journal of Mathematics and MathematicalSciences, 2006, Article ID: 48391, 1-12.
http://dx.doi.org/10.1155/ijmms/2006/48391

has been cited by the following article:

• TITLE: Fractional Optical Solitons and Fractional Noether’s Theorem with Ortigueira’s Centered Derivatives

  AUTHORS: Jorge Fujioka, Manuel Velasco, Argel Ramírez

  KEYWORDS: Fractional Derivatives, Centered Derivatives, Noether’s Theorem, Ortigueira, Optical Solitons

  JOURNAL NAME: Applied Mathematics, Vol.7 No.12, July 26, 2016

  ABSTRACT: This paper shows that the centered fractional derivatives introduced by Manuel Duarte Ortigueira in 2006 are useful in the description of optical solitons. It is shown that we can construct a fractional extension of the nonlinear Schrödinger (NLS) equation which incorporates Ortigueira’s derivatives and has soliton solutions. It is also shown that this fractional NLS equation has a Lagrangian density and can be derived from a variational principle. Finally, a fractional extension of Noether’s theorem is formulated to determine the conserved quantities associated to the invariances of the action integral under infinitesimal transformations.