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All issues Volume 16 (2021) Math. Model. Nat. Phenom., 16 (2021) 12 References
Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
Article Number 12
Number of page(s) 18
DOI https://doi.org/10.1051/mmnp/2021007
Published online 22 March 2021
  1. M. Al-Maskari and S. Karaa, Numerical approximation of semilinear subdiffusion equations with nonsmooth initial data. SIAM J. Numer. Anal. 57 (2019) 1524–1544. [Google Scholar]
  2. E. Bazhlekova, B. Jin, R. Lazarov and Z. Zhou, An analysis of the Rayleigh-Stokes problem for a generalized second-grade fluid. Numer. Math. 131 (2015) 1–31. [Google Scholar]
  3. A. Chen and C. Li, An alternating direction Galerkin method for a time-fractional partial differential equation with damping in two space dimensions. Adv. Differ. Equ. 2017 (2017) Article ID 356. [Google Scholar]
  4. E. Cuesta, C. Lubich and C. Palencia, Convolution quadrature time discretization of fractional diffusion-wave equations. Math. Comput. 75 (2006) 673–696. [Google Scholar]
  5. W. Fan, X. Jiang, F. Liu and V. Anh, The unstructured mesh finite element method for the two-dimensional multi-term time–space fractional diffusion-wave equation on an irregular convex domain. J. Sci. Comput. 77 (2018) 27–52. [Google Scholar]
  6. L. Feng, F. Liu, I. Turner and L. Zheng, Novel numerical analysis of multi-term time fractional viscoelastic non-newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid. Fract. Calc. Appl. Anal. 21 (2018) 1073–1103. [Google Scholar]
  7. L. Feng, I. Turner, P. Perré and K. Burrage, An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media. Commun. Nonlinear Sci. Numer. Simul. 92 (2020) 105454. [Google Scholar]
  8. M. Ferreira, M.M. Rodrigues and N. Vieira, Fundamental solution of the multi-dimensional time fractional telegraph equation. Fract. Calc. Appl. Anal. 20 (2017) 868–894. [Google Scholar]
  9. C. Fetecau, M. Athar and C. Fetecau, Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate. Comput. Math. Appl. 57 (2009) 596–603. [Google Scholar]
  10. W. Gao, P. Veeresha, H.M. Baskonus, D.G. Prakasha and P. Kumar, A new study of unreported cases of 2019-nCOV epidemic outbreaks. Chaos Solitons Fractals 138 (2020) 109929. [PubMed] [Google Scholar]
  11. W. Gao, P. Veeresha, D.G. Prakasha, H.M. Baskonus and G. Yel, New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function. Chaos Solitons Fractals 134 (2020) 109696. [Google Scholar]
  12. R. Gorenflo, Y. Luchko and M. Stojanović, Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Fract. Calc. Appl. Anal. 16 (2013) 297–316. [Google Scholar]
  13. B. Jin, R. Lazarov and Z. Zhou, Two fully discrete schemes for fractional diffusion and diffusion-wave equations with nonsmooth data. SIAM J. Sci. Comput. 38 (2016) A146–A170. [Google Scholar]
  14. B. Jin, B. Li and Z. Zhou, Correction of high-order BDF convolution quadrature for fractional evolution equations. SIAM J. Sci. Comput. 39 (2017) A3129–A3152. [Google Scholar]
  15. M. Khan, K. Maqbool and T. Hayat, Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space. Acta Mech. 184 (2006) 1–13. [Google Scholar]
  16. C. Li and A. Chen, Numerical methods for fractional partial differential equations. Int. J. Comput. Methods Eng. Sci. Mech. 95 (2018) 1048–1099. [Google Scholar]
  17. C. Li and F. Zeng, Numerical methods for fractional calculus. Chapman and Hall/CRC, Boca Raton (2015). [CrossRef] [Google Scholar]
  18. H. Liu and S. Lü, Gauss-Lobatto-Legendre-Birkhoff pseudospectral approximations for the multi-term time fractional diffusion-wave equation with Neumann boundary conditions. Numer. Methods Partial Differ. Equ. 34 (2018) 2217–2236. [Google Scholar]
  19. Z. Liu, F. Liu and F. Zeng, An alternating direction implicit spectral method for solving two dimensional multi-term time fractionalmixed diffusion and diffusion-wave equations. Appl. Numer. Math. 136 (2019) 139–151. [Google Scholar]
  20. C. Lubich, Convolution quadrature and discretized operational calculus. I. BIT Numer. Math. 52 (1988) 129–145. [Google Scholar]
  21. R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339 (2000) 1–77. [Google Scholar]
  22. E. Orsingher and L. Beghin, Time-fractional telegraph equations and telegraph processes with Brownian time. Probab. Theory Relat. Fields 128 (2004) 141–160. [Google Scholar]
  23. R. Schumer, D.A. Benson, M.M. Meerschaert and B. Baeumer, Fractal mobile/immobile solute transport. Water Resour. Res. 39 (2003) 1296. [Google Scholar]
  24. B. Shiri and D. Baleanu, System of fractional differential algebraic equations with applications. Chaos Solitons Fractals 120 (2019) 203–212. [Google Scholar]
  25. M. Stojanović and R. Gorenflo, Nonlinear two-term time fractional diffusion-wave problem. Nonlinear Anal.: Real World Appl. 11 (2010) 3512–3523. [Google Scholar]
  26. H. Sun, X. Zhao and Z. Sun, The temporal second order difference schemes based on the interpolation approximation for the time multi-term fractional wave equation. J. Sci. Comput. 78 (2018) 467–498. [Google Scholar]
  27. V. Thomée, Galerkin finite element methods for parabolic problems, second edn. Springer, Berlin (2006). [Google Scholar]
  28. K. Wang and Z. Zhou, High-order time stepping schemes for semilinear subdiffusion equations. SIAM J. Numer. Anal. 58 (2020) 3226–3250. [Google Scholar]
  29. F. Zeng, Z. Zhang and G.E. Karniadakis, Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions. Comput. Methods Appl. Mech. Eng. 327 (2017) 478–502. [Google Scholar]
  30. M. Zheng, F. Liu, V. Anh and I. Turner, A high-order spectral method for the multi-term time-fractional diffusion equations. Appl. Math. Model. 40 (2016) 4970–4985. [Google Scholar]

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