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In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives.
1904
Earlier work this paper cites.
Bouchaud, J.-P.; Georges, A. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195 (1990), no. 4-5, 127-293
1990
Earlier work this paper cites.
Chaos, fractional kinetics, and anomalous transport
Zaslavsky, G · 2002
Earlier work this paper cites.
Metzler, R.; Klafter, J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37 (2004), no. 31, R161-R208
2004
Earlier work this paper cites.
Lasry, J.-M.; Lions, P.-L. Mean Field Games. Jpn. J. Math., 2 (2007), 229-260
2007
Earlier work this paper cites.
Lin, Y.; Xu, C. Finite difference/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys. 225 (2007), no. 2, 1533–1552
2007
Earlier work this paper cites.
Achdou, Y.; Capuzzo Dolcetta, I. Mean field games: numerical methods. SIAM J. Numer. Anal. 48 (2010), no. 3, 1136–1162
2010
Earlier work this paper cites.
Achdou, Y.; Camilli, F.; Capuzzo Dolcetta, I. Mean field games: convergence of a finite difference method. SIAM J. Numer. Anal. 51 (2013), no. 5, 2585-2612
2013
Earlier work this paper cites.
A fractional Hamilton-Jacobi Bellman equation for scaled limits of controlled continuous time random walks
Kolokoltsov, V; Veretennikova, M · 2014
Earlier work this paper cites.
Carlini, E.; Silva, F. A semi-Lagrangian scheme for a degenerate second order mean field game system. Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4269-4292
2015
Earlier work this paper cites.
Time-fractional diffusion equation in the fractional Sobolev spaces
Gorenflo, R.; Luchko, R.; Yamamoto, M · 2015
Cited alongside, same era.
Variational formulation of problems involving fractional order differential operators
Jin, B.; Lazarov, R.; Pasciak, J; Rundell, W · 2015
Cited alongside, same era.
Achdou, Y.; Porretta, A. Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games. SIAM J. Numer. Anal. 54 (2016), 161-186
2016
Cited alongside, same era.
Annunziato, M.; Borzì, A.; Magdziarz, M.; Weron, A. A fractional Fokker-Planck control framework for subdiffusion processes. Optimal Control Appl. Methods 37 (2016), no. 2, 290-304
2016
Cited alongside, same era.
Jin, B.; Lazarov, R.; Zhou, Z. An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data. IMA J. Numer. Anal. 36 (2016), no. 1, 197-221
On existence and uniqueness of viscosity solutions for second order fully nonlinear pdes with caputo time fractional derivatives
Namba, T · 2018
Later among the works it cites.
Time-fractional Allen-Cahn equations: Analysis and numerical methods
Du, Q.; Yang, J.; Zhou, Z · 2019
Later among the works it cites.
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview
Jin, B.; Lazarov, R.; Zhou, Z · 2019
Later among the works it cites.
2019
Later among the works it cites.
Meerschaert, M.; Sikorskii, A. Stochastic Models for Fractional Calculus
2019
Later among the works it cites.
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2016
Cited alongside, same era.
Almulla, N.; Ferreira, R.; Gomes, D. Two numerical approaches to stationary mean-field games. Dyn. Games Appl. 7 (2017), no. 4, 657-682
2017
Cited alongside, same era.
Li, D.; Wang, J.; Zhang, J. Unconditionally convergent L1-Galerkin FEMs for nonlinear time-fractional Schrödinger equations. SIAM J. Sci. Comput. 39 (2017), no. 6, A3067-A3088
2017
Cited alongside, same era.
Existence and uniqueness for parabolic problems with Caputo time derivative
Topp, E.; Yangari, M. · 2017
Cited alongside, same era.
Briceño-Arias, L. M.; Kalise, D.; Silva, F. J. Proximal methods for stationary mean field games with local couplings. SIAM J. Control Optim. 56 (2018), no. 2, 801-836
2018
Cited alongside, same era.
An invitation to nonlocal modeling, analysis and computation
Du, Q · 2018
Cited alongside, same era.
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Pang, G.; Lu, L.; Karniadakis, G · 2019
Later among the works it cites.
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Shen, J.; Sheng, C.-T · 2019
Later among the works it cites.
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Tang, T.; Yu, H; Zhou., T · 2019
Later among the works it cites.
Camilli, F.; Goffi, A. Existence and regularity results for viscous Hamilton-Jacobi equations with Caputo time-fractional derivative, NoDEA Nonlinear Differential Equations Appl. 27 (2020), no. 2, Paper No. 22
2020
Closest in time.
Tang, Q. On an optimal control problem of time-fractional advection-diffusion equation. Discrete & Continuous Dynamical Systems-B, 25 (2020), 761-779
2020
Closest in time.