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Fractional calculus and continuous-time finance

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Cited by:

  1. Chu, Yu-Ming & Khan, M. Saqib & Abbas, Mujahid & Ali, Shafqat & Nazeer, Waqas, 2022. "On characterizing of bifurcation and stability analysis for time fractional glycolysis model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
  2. Valentina V. Tarasova & Vasily E. Tarasov, 2016. "Fractional Dynamics of Natural Growth and Memory Effect in Economics," Papers 1612.09060, arXiv.org, revised Jan 2017.
  3. Düring, B. & Toscani, G., 2007. "Hydrodynamics from kinetic models of conservative economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
  4. Hussam Aljarrah & Mohammad Alaroud & Anuar Ishak & Maslina Darus, 2022. "Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method," Mathematics, MDPI, vol. 10(12), pages 1-16, June.
  5. Hayashi, Katsuhiko & Kaizoji, Taisei & Pichl, Lukáš, 2007. "Correlation patterns of NIKKEI index constituents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 16-21.
  6. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2009. "Detrended fluctuation analysis of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 433-440.
  7. Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
  8. Enrico Scalas & Rudolf Gorenflo & Hugh Luckock & Francesco Mainardi & Maurizio Mantelli & Marco Raberto, 2004. "Anomalous waiting times in high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 695-702.
  9. Scalas, Enrico & Politi, Mauro, 2012. "A parsimonious model for intraday European option pricing," Economics Discussion Papers 2012-14, Kiel Institute for the World Economy (IfW Kiel).
  10. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
  11. Straka, P. & Henry, B.I., 2011. "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.
  12. Enrico Scalas, 2006. "Five Years of Continuous-time Random Walks in Econophysics," Lecture Notes in Economics and Mathematical Systems, in: Akira Namatame & Taisei Kaizouji & Yuuji Aruka (ed.), The Complex Networks of Economic Interactions, pages 3-16, Springer.
  13. Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
  14. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "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.
  15. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "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.
  16. Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
  17. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
  18. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
  19. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
  20. Fan Yang & Ping Fan & Xiao-Xiao Li & Xin-Yi Ma, 2019. "Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source," Mathematics, MDPI, vol. 7(9), pages 1-13, September.
  21. Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
  22. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
  23. Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019. "Modeling non-stationarities in high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
  24. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
  25. Scalas, Enrico, 2007. "Mixtures of compound Poisson processes as models of tick-by-tick financial data," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 33-40.
  26. Tomas Skovranek, 2019. "The Mittag-Leffler Fitting of the Phillips Curve," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
  27. Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
  28. Sazuka, Naoya & Inoue, Jun-ichi & Scalas, Enrico, 2009. "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.
  29. Almaguer, F-Javier & Amezcua, Omar González & Morales-Castillo, Javier & Soto-Villalobos, Roberto, 2018. "Riemann and Weierstrass walks revisited," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 518-526.
  30. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Dynamic intersectoral models with power-law memory," Papers 1712.09087, arXiv.org.
  31. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
  32. Hosseiny, Ali & Absalan, Mohammadreza & Sherafati, Mohammad & Gallegati, Mauro, 2019. "Hysteresis of economic networks in an XY model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 644-652.
  33. Mohamed Jleli & Bessem Samet, 2019. "Sufficient Criteria for the Absence of Global Solutions for an Inhomogeneous System of Fractional Differential Equations," Mathematics, MDPI, vol. 8(1), pages 1-8, December.
  34. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
  35. Gerd Baumann & Frank Stenger, 2017. "Fractional Fokker-Planck Equation," Mathematics, MDPI, vol. 5(1), pages 1-19, February.
  36. Marseguerra, M. & Zoia, A., 2008. "Monte Carlo evaluation of FADE approach to anomalous kinetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 345-357.
  37. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
  38. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "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.
  39. Schumer, Rina & Baeumer, Boris & Meerschaert, Mark M., 2011. "Extremal behavior of a coupled continuous time random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(3), pages 505-511.
  40. Masoliver, Jaume & Montero, Miquel & Perello, Josep & Weiss, George H., 2006. "The continuous time random walk formalism in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 577-598, December.
  41. Masanao AOKI, 2007. "Patterns of Non-exponential Growth of Macroeconomic Models: Two-Parameter Poisson-Dirichlet Models," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 115(1), pages 109-125.
  42. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
  43. Nandal, Sarita & Narain Pandey, Dwijendra, 2020. "Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay," Applied Mathematics and Computation, Elsevier, vol. 369(C).
  44. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
  45. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
  46. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
  47. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
  48. Masanao Aoki, 2008. "Growth Patterns of Two Types of Macro-Models: Limiting Behavior of One- and Two-Parameter Poisson–Dirichlet Models," Chapters, in: Roger E.A. Farmer (ed.), Macroeconomics in the Small and the Large, chapter 6, Edward Elgar Publishing.
  49. Hosseiny, Ali & Gallegati, Mauro, 2017. "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.
  50. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
  51. Tian, WenYi & Li, Can & Deng, Weihua & Wu, Yujiang, 2012. "Regularization methods for unknown source in space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 45-56.
  52. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "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.
  53. Amine, Saida & Hajri, Youssra & Allali, Karam, 2022. "A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
  54. Syed Mujahid Hussain & Sergey Osmekhin & Frédéric Délèze, 2021. "Short-term market efficiency indicator based on the waiting-time distribution," Review of Managerial Science, Springer, vol. 15(6), pages 1561-1572, August.
  55. Miccichè, S., 2016. "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.
  56. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
  57. Liu, Jun & Fu, Hongfei & Chai, Xiaochao & Sun, Yanan & Guo, Hui, 2019. "Stability and convergence analysis of the quadratic spline collocation method for time-dependent fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 633-648.
  58. Langlands, T.A.M., 2006. "Solution of a modified fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 136-144.
  59. Agarwal, Ritu & Kritika, & Purohit, Sunil Dutt, 2021. "Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
  60. David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016. "Partial chaos suppression in a fractional order macroeconomic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68.
  61. Masanao Aoki, 2006. "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.
  62. Salehi, Younes & Darvishi, Mohammad T. & Schiesser, William E., 2018. "Numerical solution of space fractional diffusion equation by the method of lines and splines," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 465-480.
  63. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
  64. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2009. "Correlated continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1194-1202, May.
  65. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
  66. D’Amico, Guglielmo & Petroni, Filippo, 2018. "Copula based multivariate semi-Markov models with applications in high-frequency finance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 765-777.
  67. Feng, L.B. & Zhuang, P. & Liu, F. & Turner, I., 2015. "Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 52-65.
  68. Plamen Ch Ivanov & Ainslie Yuen & Pandelis Perakakis, 2014. "Impact of Stock Market Structure on Intertrade Time and Price Dynamics," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-14, April.
  69. Joel Alba-Pérez & Jorge E. Macías-Díaz, 2019. "Analysis of Structure-Preserving Discrete Models for Predator-Prey Systems with Anomalous Diffusion," Mathematics, MDPI, vol. 7(12), pages 1-31, December.
  70. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "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.
  71. Bertram, William K., 2008. "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.
  72. Meerschaert, Mark M. & Scalas, Enrico, 2006. "Coupled continuous time random walks in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 114-118.
  73. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
  74. Pagnini, Gianni, 2014. "Short note on the emergence of fractional kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 29-34.
  75. Berardi, Luca & Serva, Maurizio, 2005. "Time and foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 403-412.
  76. Michelitsch, Thomas M. & Polito, Federico & Riascos, Alejandro P., 2021. "On discrete time Prabhakar-generalized fractional Poisson processes and related stochastic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
  77. Xu, Yang & Zhang, Yanming & Zhao, Jingjun, 2019. "Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 494-507.
  78. Alvaro Cartea & Thilo Meyer-Brandis, 2007. "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.
  79. Beghin, L., 2012. "Random-time processes governed by differential equations of fractional distributed order," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1314-1327.
  80. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
  81. Adán J. Serna-Reyes & Jorge E. Macías-Díaz & Nuria Reguera, 2021. "A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
  82. Zhang, Jingyuan, 2018. "A stable explicitly solvable numerical method for the Riesz fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 209-227.
  83. Shi, Dongyang & Yang, Huaijun, 2018. "Superconvergence analysis of finite element method for time-fractional Thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 31-42.
  84. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
  85. Scalas, Enrico & Viles, Noèlia, 2014. "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.
  86. Tarasov, Vasily E., 2020. "Fractional econophysics: Market price dynamics with memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
  87. Marcin Wątorek & Jarosław Kwapień & Stanisław Drożdż, 2022. "Multifractal Cross-Correlations of Bitcoin and Ether Trading Characteristics in the Post-COVID-19 Time," Future Internet, MDPI, vol. 14(7), pages 1-15, July.
  88. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
  89. Zheng, G.H. & Wei, T., 2010. "Spectral regularization method for the time fractional inverse advection–dispersion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 37-51.
  90. Jaros{l}aw Klamut & Tomasz Gubiec, 2018. "Directed Continuous-Time Random Walk with memory," Papers 1807.01934, arXiv.org.
  91. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
  92. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Concept of dynamic memory in economics," Papers 1712.09088, arXiv.org.
  93. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
  94. Caputo, Michele & Cametti, Cesare & Ruggero, Vittorio, 2008. "Time and spatial concentration profile inside a membrane by means of a memory formalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2010-2018.
  95. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
  96. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
  97. Tristan Fletcher & John Shawe-Taylor, 2013. "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.
  98. Marseguerra, M. & Zoia, A., 2007. "Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 448-464.
  99. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
  100. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
  101. Francesco Mainardi, 2020. "On the Advent of Fractional Calculus in Econophysics via Continuous-Time Random Walk," Mathematics, MDPI, vol. 8(4), pages 1-9, April.
  102. Qing Tang & Fabio Camilli, 2020. "Variational Time-Fractional Mean Field Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 573-588, June.
  103. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
  104. El-Ajou, Ahmad & Abu Arqub, Omar & Momani, Shaher & Baleanu, Dumitru & Alsaedi, Ahmed, 2015. "A novel expansion iterative method for solving linear partial differential equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 119-133.
  105. Caputo, Michele & Cametti, Cesare, 2016. "Fractional derivatives in the transport of drugs across biological materials and human skin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 705-713.
  106. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
  107. Kuroda, Koji & Murai, Joshin, 2007. "Limit theorems in financial market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 28-34.
  108. Samir A. El-Tantawy & Rasool Shah & Albandari W. Alrowaily & Nehad Ali Shah & Jae Dong Chung & Sherif. M. E. Ismaeel, 2023. "A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
  109. Scalas, Enrico, 2006. "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.
  110. Vasily E. Tarasov & Valentina V. Tarasova, 2019. "Dynamic Keynesian Model of Economic Growth with Memory and Lag," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
  111. Guo, Gang & Chen, Bin & Zhao, Xinjun & Zhao, Fang & Wang, Quanmin, 2015. "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.
  112. Repetowicz, Przemysław & Richmond, Peter, 2004. "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.
  113. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
  114. Xiufeng Yan, 2021. "Multiplicative Component GARCH Model of Intraday Volatility," Papers 2111.02376, arXiv.org.
  115. D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009. "European and American options: The semi-Markov case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194.
  116. Peiyu Yi & Feihu Huang & Jian Peng, 2019. "A Rebalancing Strategy for the Imbalance Problem in Bike-Sharing Systems," Energies, MDPI, vol. 12(13), pages 1-18, July.
  117. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2022. "Multifractal cross-correlations of bitcoin and ether trading characteristics in the post-COVID-19 time," Papers 2208.01445, arXiv.org.
  118. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
  119. Bertram, William K., 2009. "Optimal trading strategies for Itô diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2865-2873.
  120. Mura, A. & Taqqu, M.S. & Mainardi, F., 2008. "Non-Markovian diffusion equations and processes: Analysis and simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5033-5064.
  121. Gorenflo, Rudolf & Mainardi, Francesco & Vivoli, Alessandro, 2007. "Continuous-time random walk and parametric subordination in fractional diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 87-103.
  122. Inés Tejado & Emiliano Pérez & Duarte Valério, 2020. "Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
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