Abstract
In this paper, we aim to study the stochastic simulation for time and space fractional differential equations. First, we prove that the stochastic solution of the time and space fractional differential equation is a stable subordinated process driven by the stable Lévy motion. Then, the absorbent term is employed for this equation; we find the corresponding parent process yields to be driven by a tempered stable process. At last, we design an algorithm to simulate the trajectory of the proposed process. The Monte Carlo methods are also employed to get the approximated solution of the fractional differential equations. The contribution of this paper is to establish the relation between the time and space fractional differential equations and stochastic process, and provide the stochastic simulation algorithm for this fractional differential equations.
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