FracPECE swMATH ID: 24209 Software Authors: K. Diethelm, A.D. Freed Description: 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. Homepage: https://fractionalworld.wordpress.com/abstracts-fracpece/ Related Software: Matlab; FDE12; ML; FODE; Sprott's Software; DFOC; sysdfod; Mathematica; Fractional Order Chaotic Systems; RODAS; ma2dfc; Mittag-Leffler; AlexNet; MCQueue; Simulink; Ode15s; RADAR5; ParalleloGAM; Differentiation Matrix Suite; UTV Cited in: 83 Publications all top 5 Cited by 201 Authors 5 El-Saka, Hala A. A. 5 El-Sayed, Ahmed Mohamed Ahmed 3 Bera, Rasajit K. 3 Butcher, Eric A. 3 Dabiri, Arman 3 El-Mesiry, A. E. M. 3 Rajagopal, Karthikeyan 3 Saha Ray, Santanu 3 Wu, Cong 2 Ahmed, Eshag Mohamed 2 Akgul, Akif 2 Ali, Aatif 2 Băleanu, Dumitru I. 2 Diethelm, Kai 2 El Euch, Omar 2 Ford, Neville J. 2 Garrappa, Roberto 2 Hamdan, Nur ’Izzati 2 Hanyga, Andrzej 2 Higazy, M. Sh. 2 Islam, Saeed 2 Jafari, Sajad 2 Javidi, Mohammad 2 Khan, Muhammad Altaf 2 Kiliçman, Adem 2 Muhammad, Taseer 2 Pinto, Carla M. A. 2 Popolizio, Marina 2 Sarv Ahrabi, Sima 2 Shahbazi Asl, Mohammad 2 Torres, Delfim Fernando Marado 2 Zeng, Caibin 1 Abdeljawad, Thabet 1 Abdelmalek, Salem 1 Abdelouahab, Mohammed-Salah 1 Abdo, Mohammed Salem 1 Adibi, Hojatollah 1 Ahmad, Bashir 1 Akinyemi, Lanre 1 Algehyne, Ebrahem A. 1 Ali, Saeed M. 1 Alsaadi, Fawaz E. 1 Alsaadi, Fuad Eid S. 1 Alshahrani, Mohammad Y. 1 Alshehri, Maryam Gharamah Ali 1 Alshomrani, Ali Saleh 1 Aqeel, Muhammad 1 Area, Iván 1 Arslan, Damla 1 Babolian, Esmail 1 Barbosa, A. N. 1 Baskonus, Haci Mehmet 1 Batarfi, Hanan 1 Bebbouchi, Rachid 1 Bendoukha, Samir 1 Bologna, Mauro 1 Boyraz, Ömer Faruk 1 Braga, Joao Paulo 1 Brummund, Jörg 1 Bulut, Hasan 1 Burrage, Kevin 1 Camargo, Rubens F. 1 Carvalho, Ana R. M. 1 Čermák, Jan 1 Chaudhuri, Kripa Sindhu 1 Chen, Hsien-Keng 1 Chen, Juhn-Horng 1 Chen, Wen-Chin 1 Chidouh, Amar 1 Dos Santos, José Paulo Carvalho 1 Douaifia, Redouane 1 D’Ovidio, Mirko 1 Drăgănescu, Gheorghe 1 Durdu, Ali 1 Effati, Sohrab 1 El-Beltagy, Mohamed A. 1 El-Mesady, Ahmed 1 Eshaghi, Jafar 1 Etman, Ahmed 1 Fang, Hui 1 Ferreira, José Claudinei 1 Fiaz, Muhammad Arshad 1 Ford, Judith M. 1 Grigolini, Paolo 1 Guezane-Lakoud, Assia 1 Habbireeh, Rafla 1 Hamri, Nasreddine 1 He, Shaobo 1 Helikumi, Mlyashimbi 1 Henry, Bruce I. 1 Hofmann, Bernd 1 Iyiola, Olaniyi Samuel 1 Jaber, Eduardo Abi 1 Jahanshahi, Salman 1 Jajarmi, Amin 1 Jannelli, Alessandra 1 Jarad, Fahd 1 Jesus, Carla 1 Kamyad, Ali Vahidian 1 Kang, Yuan ...and 101 more Authors all top 5 Cited in 41 Serials 12 Chaos, Solitons and Fractals 5 Applied Mathematics and Computation 5 Journal of Computational and Applied Mathematics 5 Nonlinear Dynamics 4 Communications in Nonlinear Science and Numerical Simulation 4 Advances in Difference Equations 3 Mathematics and Computers in Simulation 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Computational and Applied Mathematics 2 Journal of Computational Physics 2 Applied Mathematical Modelling 2 Fractals 2 Mathematical Problems in Engineering 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Mediterranean Journal of Mathematics 1 Acta Mechanica 1 Journal of Mathematical Analysis and Applications 1 Physica A 1 Bulletin of Mathematical Biology 1 Physica D 1 Computational Mechanics 1 Applied Mathematics Letters 1 Signal Processing 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 Continuum Mechanics and Thermodynamics 1 Journal of the Egyptian Mathematical Society 1 Mathematical Finance 1 Vietnam Journal of Mathematics 1 Chaos 1 Fractional Calculus & Applied Analysis 1 Discrete Dynamics in Nature and Society 1 Dynamics of Continuous, Discrete & Impulsive Systems. 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