# Fractional calculus and continuous-time finance

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
**Cited by:**

- Valentina V. Tarasova & Vasily E. Tarasov, 2016.
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**Fractional Dynamics of Natural Growth and Memory Effect in Economics**," Papers 1612.09060, arXiv.org, revised Jan 2017. - Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2009.
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**Correlated continuous time random walks**," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1194-1202, May. - Hayashi, Katsuhiko & Kaizoji, Taisei & Pichl, Lukáš, 2007.
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**Correlation patterns of NIKKEI index constituents**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 16-21. - repec:eee:ejores:v:267:y:2018:i:2:p:765-777 is not listed on IDEAS
- repec:eee:apmaco:v:257:y:2015:i:c:p:52-65 is not listed on IDEAS
- Scalas, Enrico & Politi, Mauro, 2012.
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**A parsimonious model for intraday European option pricing**," Economics Discussion Papers 2012-14, Kiel Institute for the World Economy (IfW).- Enrico Scalas & Mauro Politi, 2012.
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**A parsimonious model for intraday European option pricing**," Papers 1202.4332, arXiv.org.

- Enrico Scalas & Mauro Politi, 2012.
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- Straka, P. & Henry, B.I., 2011.
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**Lagging and leading coupled continuous time random walks, renewal times and their joint limits**," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 324-336, February. - Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000.
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**Fractional calculus and continuous-time finance II: the waiting-time distribution**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000.
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**Fractional calculus and continuous-time finance II: the waiting-time distribution**," Papers cond-mat/0006454, arXiv.org, revised Nov 2000. - Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004.
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**Fractional calculus and continuous-time finance II: the waiting- time distribution**," Finance 0411008, EconWPA.

- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000.
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- Bertram, William K., 2008.
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**Measuring time dependent volatility and cross-sectional correlation in Australian equity returns**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3183-3191. - Enrico Scalas, 2005.
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**Five Years of Continuous-time Random Walks in Econophysics**," Papers cond-mat/0501261, arXiv.org.- Enrico Scalas, 2005.
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**Five Years of Continuous-time Random Walks in Econophysics**," Finance 0501005, EconWPA.

- Enrico Scalas, 2005.
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- Meerschaert, Mark M. & Scalas, Enrico, 2006.
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**Coupled continuous time random walks in finance**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 114-118.- Mark M. Meerschaert & Enrico Scalas, 2006.
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**Coupled continuous time random walks in finance**," Papers physics/0608281, arXiv.org.

- Mark M. Meerschaert & Enrico Scalas, 2006.
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- Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002.
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**Waiting-times and returns in high-frequency financial data: an empirical study**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.- M. Raberto & E. Scalas & F. Mainardi, 2002.
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**Waiting-times and returns in high-frequency financial data: an empirical study**," Papers cond-mat/0203596, arXiv.org. - Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004.
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**Waiting-times and returns in high-frequency financial data: an empirical study**," Finance 0411014, EconWPA.

- M. Raberto & E. Scalas & F. Mainardi, 2002.
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- Pagnini, Gianni, 2014.
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**Short note on the emergence of fractional kinetics**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 29-34. - Berardi, Luca & Serva, Maurizio, 2005.
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**Time and foreign exchange markets**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 403-412. - Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010.
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**Pricing bounds for discrete arithmetic Asian options under Lévy models**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207. - Alvaro Cartea & Thilo Meyer-Brandis, 2007.
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**How Does Duration Between Trades of Underlying Securities Affect Option Prices**," Birkbeck Working Papers in Economics and Finance 0721, Birkbeck, Department of Economics, Mathematics & Statistics. - Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006.
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**Waiting times between orders and trades in double-auction markets**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.- Enrico Scalas & Taisei Kaizoji & Michael Kirchler & Juergen Huber & Alessandra Tedeschi, 2006.
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**Waiting times between orders and trades in double-auction markets**," Papers physics/0608273, arXiv.org.

- Enrico Scalas & Taisei Kaizoji & Michael Kirchler & Juergen Huber & Alessandra Tedeschi, 2006.
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- Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008.
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**Triangular array limits for continuous time random walks**," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September. - repec:eee:apmaco:v:323:y:2018:i:c:p:31-42 is not listed on IDEAS
- Scalas, Enrico & Viles, Noèlia, 2014.
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**A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process**," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410. - Fei Ren & Gao-Feng Gu & Wei-Xing Zhou, 2009.
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**Scaling and memory in the return intervals of realized volatility**," Papers 0904.1107, arXiv.org, revised Aug 2009. - Masoliver, Jaume & Montero, Miquel & Perello, Josep & Weiss, George H., 2006.
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**The continuous time random walk formalism in financial markets**," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 577-598, December.- Jaume Masoliver & Miquel Montero & Josep Perello, "undated".
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**The continuous time random walk formalism in financial markets**," Modeling, Computing, and Mastering Complexity 2003 24, Society for Computational Economics. - J. Masoliver & M. Montero & J. Perello & G. H. Weiss, 2006.
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**The continuous time random walk formalism in financial markets**," Papers physics/0611138, arXiv.org.

- Jaume Masoliver & Miquel Montero & Josep Perello, "undated".
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- Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007.
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**Fractional diffusion models of option prices in markets with jumps**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.- Alvaro Cartea & Diego del-Castillo-Negrete, 2006.
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**Fractional Diffusion Models of Option Prices in Markets with Jumps**," Birkbeck Working Papers in Economics and Finance 0604, Birkbeck, Department of Economics, Mathematics & Statistics.

- Alvaro Cartea & Diego del-Castillo-Negrete, 2006.
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- Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006.
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**Fractional vector calculus for fractional advection–dispersion**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190. - Zheng, G.H. & Wei, T., 2010.
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**Spectral regularization method for the time fractional inverse advection–dispersion equation**," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 37-51. - Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2009.
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**Detrended fluctuation analysis of intertrade durations**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 433-440. - Valentina V. Tarasova & Vasily E. Tarasov, 2017.
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**Concept of dynamic memory in economics**," Papers 1712.09088, arXiv.org. - Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006.
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**Growth and allocation of resources in economics: The agent-based approach**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.- Enrico Scalas & Mauro Gallegati & Eric Guerci & David Mas & Alessandra Tedeschi, 2006.
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**Growth and Allocation of Resources in Economics: The Agent-Based Approach**," Papers physics/0608221, arXiv.org. - Eric Guerci & Enrico Scalas & Mauro Gallegati & David Mas & Alessandra Tedeschi, 2006.
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**Growth and allocation of resources in economics: The agent-based approach**," Post-Print halshs-00871047, HAL.

- Enrico Scalas & Mauro Gallegati & Eric Guerci & David Mas & Alessandra Tedeschi, 2006.
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- Valentina V. Tarasova & Vasily E. Tarasov, 2017.
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**Logistic map with memory from economic model**," Papers 1712.09092, arXiv.org. - Sazuka, Naoya & Inoue, Jun-ichi & Scalas, Enrico, 2009.
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**The distribution of first-passage times and durations in FOREX and future markets**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2839-2853.- Naoya Sazuka & Jun-ichi Inoue & Enrico Scalas, 2008.
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**The distribution of first-passage times and durations in FOREX and future markets**," Papers 0808.0372, arXiv.org.

- Naoya Sazuka & Jun-ichi Inoue & Enrico Scalas, 2008.
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- repec:eee:apmaco:v:319:y:2018:i:c:p:518-526 is not listed on IDEAS
- Valentina V. Tarasova & Vasily E. Tarasov, 2017.
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**Dynamic intersectoral models with power-law memory**," Papers 1712.09087, arXiv.org. - Tristan Fletcher & John Shawe-Taylor, 2013.
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**Multiple Kernel Learning with Fisher Kernels for High Frequency Currency Prediction**," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 217-240, August. - Álvaro Cartea & Thilo Meyer-Brandis, 2010.
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**How Duration Between Trades of Underlying Securities Affects Option Prices**," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.- Cartea, Álvaro & Meyer-Brandis, Thilo, 2009.
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**How Duration Between Trades of Underlying Securities Affects Option Prices**," MPRA Paper 16179, University Library of Munich, Germany.

- Cartea, Álvaro & Meyer-Brandis, Thilo, 2009.
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- Guglielmo D'Amico & Filippo Petroni, 2013.
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**Multivariate high-frequency financial data via semi-Markov processes**," Papers 1305.0436, arXiv.org. - Schumer, Rina & Baeumer, Boris & Meerschaert, Mark M., 2011.
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**Extremal behavior of a coupled continuous time random walk**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(3), pages 505-511. - Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010.
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**Scaling and memory in the non-Poisson process of limit order cancelation**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761. - Foad Shokrollahi, 2016.
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**Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs**," Papers 1612.06665, arXiv.org, revised Aug 2017. - Kuroda, Koji & Murai, Joshin, 2007.
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**Limit theorems in financial market models**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 28-34. - Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005.
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**Models of anomalous diffusion: the subdiffusive case**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420. - Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008.
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**Scaling in the distribution of intertrade durations of Chinese stocks**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825. - Scalas, Enrico, 2006.
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**The application of continuous-time random walks in finance and economics**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239. - Guo, Gang & Chen, Bin & Zhao, Xinjun & Zhao, Fang & Wang, Quanmin, 2015.
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**First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 279-290. - Hosseiny, Ali & Gallegati, Mauro, 2017.
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**Role of intensive and extensive variables in a soup of firms in economy to address long run prices and aggregate data**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 51-59.- Ali Hosseiny & Mauro Gallegati, 2016.
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**Role of Intensive and Extensive Variables in a Soup of Firms in Economy to Address Long Run Prices and Aggregate Data**," Papers 1608.02523, arXiv.org, revised Jan 2017.

- Ali Hosseiny & Mauro Gallegati, 2016.
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- Repetowicz, Przemysław & Richmond, Peter, 2004.
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**Modeling of waiting times and price changes in currency exchange data**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 677-693. - D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009.
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**European and American options: The semi-Markov case**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194. - Tian, WenYi & Li, Can & Deng, Weihua & Wu, Yujiang, 2012.
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**Regularization methods for unknown source in space fractional diffusion equation**," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 45-56. - Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012.
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**Time-changed geometric fractional Brownian motion and option pricing with transaction costs**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977. - Masanao Aoki, 2006.
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**Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models**," CIRJE F-Series CIRJE-F-449, CIRJE, Faculty of Economics, University of Tokyo. - Bertram, William K., 2009.
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**Optimal trading strategies for Itô diffusion processes**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2865-2873. - Mura, A. & Taqqu, M.S. & Mainardi, F., 2008.
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**Non-Markovian diffusion equations and processes: Analysis and simulations**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5033-5064. - Miccichè, S., 2016.
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**Understanding the determinants of volatility clustering in terms of stationary Markovian processes**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 186-197. - Ali Balcı, Mehmet, 2017.
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**Time fractional capital-induced labor migration model**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98. - Langlands, T.A.M., 2006.
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**Solution of a modified fractional diffusion equation**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 136-144. - David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016.
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**Partial chaos suppression in a fractional order macroeconomic model**," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68. - Masanao Aoki, 2006.
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**Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models (Forthcoming in "Rivista Internazionale di Scienze Sociali", cxv No.1, pp. 109-125, 2007. )**," CARF F-Series CARF-F-085, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo. - Barbieri, Davide & Vivoli, Alessandro, 2005.
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**Long-range correlations in time series generated by time-fractional diffusion: A numerical study**," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 190-198. - Valentina V. Tarasova & Vasily E. Tarasov, 2016.
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**Economic Accelerator with Memory: Discrete Time Approach**," Papers 1612.07913, arXiv.org, revised Jul 2017.