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. Čermák, Jan; Nechvátal, Luděk: Local bifurcations and chaos in the fractional Rössler system (2018)
  2. 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)
  3. Popolizio, Marina: Numerical solution of multiterm fractional differential equations using the matrix Mittag-Leffler functions (2018)
  4. Sarv Ahrabi, Sima; Momenzadeh, Alireza: On failed methods of fractional differential equations: the case of multi-step generalized differential transform method (2018)
  5. Zhu, Huijian; Zeng, Caibin: A novel chaotification scheme for fractional system and its application (2018)
  6. Dabiri, Arman; Butcher, Eric A.: Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations (2017)
  7. Eshaghi, Jafar; Adibi, Hojatollah; Kazem, Saeed: On a numerical investigation of the time fractional Fokker-Planck equation via local discontinuous Galerkin method (2017)
  8. Jahanshahi, S.; Babolian, E.; Torres, D. F. M.; Vahidi, A. R.: A fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives (2017)
  9. Lin, Xiaofang; Liao, Binghui; Zeng, Caibin: The onset of chaos via asymptotically period-doubling cascade in fractional order Lorenz system (2017)
  10. Chidouh, Amar; Guezane-Lakoud, Assia; Bebbouchi, Rachid: Positive solutions of the fractional relaxation equation using lower and upper solutions (2016)
  11. Mohamed, Adel S.; Mahmoud, R. A.: Picard, Adomian and predictor-corrector methods for an initial value problem of arbitrary (fractional) orders differential equation (2016)
  12. Area, Ivan; Batarfi, Hanan; Losada, Jorge; Nieto, Juan J.; Shammakh, Wafa; Torres, Ángela: On a fractional order Ebola epidemic model (2015)
  13. Baskonus, Haci Mehmet; Bulut, Hasan: On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method (2015)
  14. Bologna, Mauro; Svenkeson, Adam; West, Bruce J.; Grigolini, Paolo: Diffusion in heterogeneous media: an iterative scheme for finding approximate solutions to fractional differential equations with time-dependent coefficients (2015)
  15. Garrappa, Roberto; Popolizio, Marina: Exponential quadrature rules for linear fractional differential equations (2015)
  16. Tian, Jinglei; Yu, Yongguang; Wang, Hu: Stability and bifurcation of two kinds of three-dimensional fractional Lotka-Volterra systems (2014)
  17. Yu, Q.; Liu, F.; Turner, I.; Burrage, K.: Numerical simulation of the fractional Bloch equations (2014)
  18. Müller, Sebastian; Kästner, Markus; Brummund, Jörg; Ulbricht, Volker: On the numerical handling of fractional viscoelastic material models in a FE analysis (2013)
  19. Zhang, Kun; Wang, Hua; Fang, Hui: Feedback control and hybrid projective synchronization of a fractional-order Newton-Leipnik system (2012)
  20. Magin, Richard; Ortigueira, Manuel D.; Podlubny, Igor; Trujillo, Juan: On the fractional signals and systems (2011)

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