The FracPECE subroutine for the numerical solution of differential equations of fractional order. We present and discuss an algorithm for the numerical solution of nonlinear differential equations of fractional (i.e., non-integer) order. This algorithm allows us to analyze in an efficient way a mathematical model for the description of the behaviour of viscoplastic materials. The model contains a nonlinear differential equation of order β, where β is a material constant typically in the range 0 < β < 1. This equation is coupled with a first-order differential equation. The algorithm for the numerical solution of these equations is based on a PECE-type approach.

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  1. Baleanu, D.; Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.: A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator (2019)
  2. El Euch, Omar; Rosenbaum, Mathieu: The characteristic function of rough Heston models (2019)
  3. Jaber, Eduardo Abi; El Euch, Omar: Multifactor approximation of rough volatility models (2019)
  4. Shahbazi Asl, Mohammad; Javidi, Mohammad: A new numerical method for solving system of FDEs: applied in plankton system (2019)
  5. Zhang, Ye; Hofmann, Bernd: On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces (2019)
  6. Čermák, Jan; Nechvátal, Luděk: Local bifurcations and chaos in the fractional Rössler system (2018)
  7. Hamdan, Nur ’Izzati; Kilicman, Adem: A fractional order SIR epidemic model for dengue transmission (2018)
  8. Jannelli, Alessandra; Ruggieri, Marianna; Speciale, Maria Paola: Exact and numerical solutions of time-fractional advection-diffusion equation with a nonlinear source term by means of the Lie symmetries (2018)
  9. Popolizio, Marina: Numerical solution of multiterm fractional differential equations using the matrix Mittag-Leffler functions (2018)
  10. Sarv Ahrabi, Sima; Momenzadeh, Alireza: On failed methods of fractional differential equations: the case of multi-step generalized differential transform method (2018)
  11. Zeid, Samaneh Soradi; Effati, Sohrab; Kamyad, Ali Vahidian: Approximation methods for solving fractional optimal control problems (2018)
  12. Zhu, Huijian; Zeng, Caibin: A novel chaotification scheme for fractional system and its application (2018)
  13. Ameen, I.; Novati, P.: The solution of fractional order epidemic model by implicit Adams methods (2017)
  14. Dabiri, Arman; Butcher, Eric A.: Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations (2017)
  15. Eshaghi, Jafar; Adibi, Hojatollah; Kazem, Saeed: On a numerical investigation of the time fractional Fokker-Planck equation via local discontinuous Galerkin method (2017)
  16. Jahanshahi, S.; Babolian, E.; Torres, D. F. M.; Vahidi, A. R.: A fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives (2017)
  17. Lin, Xiaofang; Liao, Binghui; Zeng, Caibin: The onset of chaos via asymptotically period-doubling cascade in fractional order Lorenz system (2017)
  18. Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhao, Hui: Finite-time projective synchronization of memristor-based delay fractional-order neural networks (2017)
  19. Chidouh, Amar; Guezane-Lakoud, Assia; Bebbouchi, Rachid: Positive solutions of the fractional relaxation equation using lower and upper solutions (2016)
  20. Mohamed, Adel S.; Mahmoud, R. A.: Picard, Adomian and predictor-corrector methods for an initial value problem of arbitrary (fractional) orders differential equation (2016)

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