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. Maurício de Carvalho, João P. S.; Pinto, Carla M. A.: Role of the immune system in AIDS-defining malignancies (2022)
  2. Cardoso, Lislaine Cristina; Camargo, Rubens Figueiredo; dos Santos, Fernando Luiz Pio; Dos Santos, José Paulo Carvalho: Global stability analysis of a fractional differential system in hepatitis B (2021)
  3. Douaifia, Redouane; Bendoukha, Samir; Abdelmalek, Salem: A Newton interpolation based predictor-corrector numerical method for fractional differential equations with an activator-inhibitor case study (2021)
  4. Higazy, M.; El-Mesady, A.; Mahdy, A. M. S.; Ullah, Sami; Al-Ghamdi, A.: Numerical, approximate solutions, and optimal control on the deathly Lassa hemorrhagic fever disease in pregnant women (2021)
  5. Iyiola, Olaniyi; Oduro, Bismark; Akinyemi, Lanre: Analysis and solutions of generalized chagas vectors re-infestation model of fractional order type (2021)
  6. Jesus, Carla; Sousa, Ercília: Numerical solutions for asymmetric Lévy flights (2021)
  7. Kumar, Surendra; Sharma, Abhishek; Pal Singh, Harendra: Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay (2021)
  8. Mahmoud, Emad E.; Higazy, M.; Alotaibi, Hammad; Abo-Dahab, S. M.; Abdel-Khalek, S.; Khalil, E. M.: Quaternion anti-synchronization of a novel realizable fractional chaotic model (2021)
  9. Ndaïrou, Faïçal; Area, Iván; Nieto, Juan J.; Silva, Cristiana J.; Torres, Delfim F. M.: Fractional model of COVID-19 applied to Galicia, Spain and Portugal (2021)
  10. 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)
  11. Wu, Cong: Advances in analysis of Caputo fractional-order nonautonomous systems: from stability to global uniform asymptotic stability (2021)
  12. Zhang, Xiao-Hong; Ali, Aatif; Khan, Muhammad Altaf; Alshahrani, Mohammad Y.; Muhammad, Taseer; Islam, Saeed: Mathematical analysis of the TB model with treatment via Caputo-type fractional derivative (2021)
  13. Abdo, Mohammed S.; Abdeljawad, Thabet; Ali, Saeed M.; Shah, Kamal; Jarad, Fahd: Existence of positive solutions for weighted fractional order differential equations (2020)
  14. Helikumi, Mlyashimbi; Kgosimore, Moatlhodi; Kuznetsov, Dmitry; Mushayabasa, Steady: A fractional-order \textitTrypanosomabrucei rhodesiense model with vector saturation and temperature dependent parameters (2020)
  15. Higazy, M.: Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic (2020)
  16. 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)
  17. Owusu-Mensah, Isaac; Akinyemi, Lanre; Oduro, Bismark; Iyiola, Olaniyi S.: A fractional order approach to modeling and simulations of the novel COVID-19 (2020)
  18. Pinto, Carla M. A.; Carvalho, Ana R. M.: Analysis of a non-integer order model for the coinfection of HIV and HSV-2 (2020)
  19. Asl, Mohammad Shahbazi; Javidi, Mohammad; Ahmad, Bashir: New predictor-corrector approach for nonlinear fractional differential equations: error analysis and stability (2019)
  20. 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)

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