Non-Local Pseudo-Differential Operators
  We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous equations associated with these operators. We also extend the formalism to d-dimensional space-time solving, in particular, the fractional Wave and Klein-Gordon equations. 
D. G. Barci, C. G. Bollini, L. E. Oxman and M. C. Rocca