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1. A finite-difference solution of mean field problem with the fractional derivative for subdiffusion.

Author

Shaydurov, V. V., Zhang, S., Kornienko, V. S., and Todorov, Michail D

Subjects
*FINITE differences, *PARABOLIC differential equations, *HAMILTON-Jacobi-Bellman equation, *MEAN field theory, *FOKKER-Planck equation, *RIESZ spaces, *ALGORITHMS
Abstract

The paper presents a computational algorithm for solving problems formulated in terms of Mean Field Game theory with diffusion expressed by fractional derivative. The Mean Field equilibrium leads to a coupled system of two parabolic partial differential equations: modified Fokker-Planck-Kolmogorov and Hamilton-Jacobi-Bellman equations with the highest derivative in space of fractional order less than 2. The article is devoted to the discrete approximation of these equations and the computational algorithm for solving discrete analogues. [ABSTRACT FROM AUTHOR]

Published
2020
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