Monte Carlo method for fractional-order differentiation
Nikolai Leonenko, Igor Podlubný
Abstract
Abstract In this work the Monte Carlo method is introduced for numerical evaluation of fractional-order derivatives. A general framework for using this method is presented and illustrated by several examples. The proposed method can be used for numerical evaluation of the Grünwald-Letnikov fractional derivatives, the Riemann-Liouville fractional derivatives, and also of the Caputo fractional derivatives, when they are equivalent to the Riemann-Liouville derivatives. The proposed method can be enhanced using standard approaches for the classic Monte Carlo method, and it also allows easy parallelization, which means that it is of high potential for applications of the fractional calculus.
Topics & Concepts
MathematicsFractional calculusMonte Carlo methodQuasi-Monte Carlo methodApplied mathematicsOrder (exchange)Hybrid Monte CarloCalculus (dental)Markov chain Monte CarloStatisticsEconomicsDentistryMedicineFinanceFractional Differential Equations SolutionsMathematical functions and polynomialsNumerical methods for differential equations