Advances in fractional calculus J Sabatier, OP Agrawal, JAT Machado Springer 4 (9), 2007 | 2848 | 2007 |

Recent history of fractional calculus JT Machado, V Kiryakova, F Mainardi Communications in nonlinear science and numerical simulation 16 (3), 1140-1153, 2011 | 1730 | 2011 |

Fractional dynamics and control D Baleanu, JAT Machado, ACJ Luo Springer Science & Business Media, 2011 | 922 | 2011 |

New trends in nanotechnology and fractional calculus applications D Baleanu, ZB Güvenç, JAT Machado Springer 10, 978-90, 2010 | 873 | 2010 |

Towards the development of intelligent transportation systems L Figueiredo, I Jesus, JAT Machado, JR Ferreira, JLM De Carvalho ITSC 2001. 2001 IEEE intelligent transportation systems. Proceedings (Cat …, 2001 | 656 | 2001 |

A review of definitions for fractional derivatives and integral EC De Oliveira, JA Tenreiro Machado Mathematical Problems in Engineering 2014, 2014 | 594 | 2014 |

Analysis and design of fractional-order digital control systems JAT Machado Systems Analysis Modelling Simulation 27 (2-3), 107-122, 1997 | 582 | 1997 |

The role of fractional calculus in modeling biological phenomena: A review C Ionescu, A Lopes, D Copot, JAT Machado, JHT Bates Communications in Nonlinear Science and Numerical Simulation 51, 141-159, 2017 | 538 | 2017 |

What is a fractional derivative? MD Ortigueira, JAT Machado Journal of computational Physics 293, 4-13, 2015 | 499 | 2015 |

Tuning of PID controllers based on Bode’s ideal transfer function RS Barbosa, JAT Machado, IM Ferreira Nonlinear dynamics 38, 305-321, 2004 | 379 | 2004 |

Some applications of fractional calculus in engineering JA Tenreiro Machado, MF Silva, RS Barbosa, IS Jesus, CM Reis, ... Mathematical problems in engineering 2010, 2010 | 367 | 2010 |

A review of definitions of fractional derivatives and other operators GS Teodoro, JAT Machado, EC De Oliveira Journal of Computational Physics 388, 195-208, 2019 | 365 | 2019 |

Discrete-time fractional-order controllers JA Machado Fractional Calculus and Applied Analysis 4, 47-66, 2001 | 317 | 2001 |

Fractional order calculus: basic concepts and engineering applications RE Gutierrez, JM Rosário, J Tenreiro Machado Mathematical problems in engineering 2010, 2010 | 306 | 2010 |

Development of fractional order capacitors based on electrolyte processes IS Jesus, JA Tenreiro Machado Nonlinear Dynamics 56, 45-55, 2009 | 279 | 2009 |

Particle swarm optimization with fractional-order velocity EJ Solteiro Pires, JA Tenreiro Machado, PB de Moura Oliveira, ... Nonlinear Dynamics 61, 295-301, 2010 | 260 | 2010 |

A new fractional operator of variable order: application in the description of anomalous diffusion XJ Yang, JAT Machado Physica A: Statistical Mechanics and its Applications 481, 276-283, 2017 | 252 | 2017 |

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation XJ Yang, JA Tenreiro Machado, D Baleanu, C Cattani Chaos: An Interdisciplinary Journal of Nonlinear Science 26 (8), 2016 | 242 | 2016 |

Fractional control of heat diffusion systems IS Jesus, JA Tenreiro Machado Nonlinear dynamics 54, 263-282, 2008 | 238 | 2008 |

Fractional calculus: A survey of useful formulas D Valério, JJ Trujillo, M Rivero, JAT Machado, D Baleanu The European Physical Journal Special Topics 222 (8), 1827-1846, 2013 | 236 | 2013 |