Green's Theorem for Generalized Fractional Derivatives
arXiv:1205.4851 · doi:10.2478/s13540-013-0005-z
Abstract
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.
This is a preprint of a paper whose final and definite form will appear at http://www.springerlink.com: Fract. Calc. Appl. Anal. 16 (2013), no. 1, in press. Submitted 09-July-2012; accepted, after a revision, 24-Oct-2012