Fokker Planck equation solved in terms of complex fractional moments

• Solution of Fokker Planck equation in terms of complex fractional moments.
• Complex fractional moments for different values of the real part of the exponent in the Mellin transform.
• Probability density function as a solution of the Fokker Planck equation obtained by solving a linear set of ODE.
• Procedure available for initial and boundary value problems.

In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones, the solution of the FPK equation in terms of a finite number of complex moments may be easily found. It is shown that the probability density function (PDF) solution of the FPK equation is restored in the whole domain, including the trend at infinity with the exception of the value of the PDF in zero.