Affiliation:
1. Physics Department, United Arab Emirates University, UAE
Abstract
The transformation properties of the fractional derivatives under spatial rotation in two-dimensional space and for both the Riemann-Liouville and Caputo definitions are investigated and derived in their general form. In particular, the transformation properties of the fractional derivatives acting on scalar fields are studied and discussed. The study of the transformation properties of fractional derivatives is an essential step for the formulation of fractional calculus in multi-dimensional space. The inclusion of fractional calculus in the Lagrangian and Hamiltonian dynamical formulation relies on such transformation. Specific examples on the transformation of the fractional derivatives of scalar fields are discussed.
Reference45 articles.
1. Geometric Interpretation of the Fractional Derivative.;F. B.Adda;Journal of Fractional Calculus,1997
2. The Differentiability in the Fractional Calculus.;F. B.Adda;Nonlinear Analysis,2001
3. Formulation of Euler–Lagrange equations for fractional variational problems