In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schrödinger and Dirac equations.

• Received 25 February 2011

DOI:https://doi.org/10.1103/PhysRevA.83.062109