Green's theorem for generalized fractional derivatives

Abstract

We study three types of generalized partial fractional order 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. © 2013 Versita Warsaw and Springer-Verlag Wien.