Geodesic
Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation
Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 47-56.

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A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.
Keywords: Fractional Partial Differential Equations, Stochastic Solutions, 26A33, 76M35, 82B31 
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Cipriano, F.; Ouerdiane, H.; Vilela Mendes, R. Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation. Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 47-56. http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a3/