FracPECE

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.


References in zbMATH (referenced in 53 articles )

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  1. Tavares, Camila A.; Santos, Taináh M. R.; Lemes, Nelson H. T.; dos Santos, José P. C.; Ferreira, José C.; Braga, João P.: Solving ill-posed problems faster using fractional-order Hopfield neural network (2021)
  2. Milici, Constantin; Machado, José Tenreiro; Drăgănescu, Gheorghe: Application of the Euler and Runge-Kutta generalized methods for FDE and symbolic packages in the analysis of some fractional attractors (2020)
  3. 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)
  4. El Euch, Omar; Rosenbaum, Mathieu: The characteristic function of rough Heston models (2019)
  5. Jaber, Eduardo Abi; El Euch, Omar: Multifactor approximation of rough volatility models (2019)
  6. Rajagopal, Karthikeyan; Akgul, Akif; Pham, Viet-Thanh; Alsaadi, Fawaz E.; Nazarimehr, Fahimeh; Alsaadi, Fuad E.; Jafari, Sajad: Multistability and coexisting attractors in a new circulant chaotic system (2019)
  7. Ren, Jiaojiao; Wu, Cong: Advances in Lyapunov theory of Caputo fractional-order systems (2019)
  8. Shahbazi Asl, Mohammad; Javidi, Mohammad: A new numerical method for solving system of FDEs: applied in plankton system (2019)
  9. Wu, Cong; Liu, Xinzhi: Lyapunov and external stability of Caputo fractional order switching systems (2019)
  10. Zhang, Ye; Hofmann, Bernd: On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces (2019)
  11. Čermák, Jan; Nechvátal, Luděk: Local bifurcations and chaos in the fractional Rössler system (2018)
  12. Dabiri, Arman; Butcher, Eric A.: Numerical solution of multi-order fractional differential equations with multiple delays via spectral collocation methods (2018)
  13. Hamdan, Nur ’Izzati; Kilicman, Adem: A fractional order SIR epidemic model for dengue transmission (2018)
  14. 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)
  15. Popolizio, Marina: Numerical solution of multiterm fractional differential equations using the matrix Mittag-Leffler functions (2018)
  16. Sarv Ahrabi, Sima; Momenzadeh, Alireza: On failed methods of fractional differential equations: the case of multi-step generalized differential transform method (2018)
  17. Zeid, Samaneh Soradi; Effati, Sohrab; Kamyad, Ali Vahidian: Approximation methods for solving fractional optimal control problems (2018)
  18. Zhu, Huijian; Zeng, Caibin: A novel chaotification scheme for fractional system and its application (2018)
  19. Ameen, I.; Novati, P.: The solution of fractional order epidemic model by implicit Adams methods (2017)
  20. Dabiri, Arman; Butcher, Eric A.: Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations (2017)

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