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J. A. Tenreiro Machado

J. A. Tenreiro Machado

Polytechnic Institute of Porto
Portugal

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Electronics and Electrical Engineering
Portugal
2026
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Mathematics
Portugal
2026

D-Index & Metrics

Discipline name D-Index World Ranking Current World Ranking National Ranking Current National Ranking Publications Citations
Mathematics 89 79 64 1 1 786 36256
Electronics and Electrical Engineering 72 795 758 3 3 634 24943

J. A. Tenreiro Machado publications per year

The chart shows the history of publications by J. A. Tenreiro Machado between 1988 and 2025, highlighting the no. of papers published in each year and offering an overview of the publication velocity of this scholar. J. A. Tenreiro Machado published across 38 years, from 1988 to 2025, averaging 24.1 papers a year. Output peaked at 72 publications in 2019. 19 of the 914 publications appeared in the last two years.

No. of publications
20 40 60
Bar chart. Horizontal axis: year, 1988 to 2025. Vertical axis: number of publications, 0 to 72. Peak 72 publications in 2019. 1988: 7 publications 1989: 1 publication 1990: 6 publications 1991: 6 publications 1992: 1 publication 1993: 5 publications 1994: 1 publication 1995: 2 publications 1996: 1 publication 1997: 12 publications 1998: 11 publications 1999: 5 publications 2000: 10 publications 2001: 6 publications 2002: 8 publications 2003: 11 publications 2004: 25 publications 2005: 15 publications 2006: 29 publications 2007: 32 publications 2008: 28 publications 2009: 41 publications 2010: 34 publications 2011: 50 publications 2012: 35 publications 2013: 55 publications 2014: 37 publications 2015: 44 publications 2016: 47 publications 2017: 50 publications 2018: 41 publications 2019: 72 publications 2020: 69 publications 2021: 66 publications 2022: 30 publications 2023: 2 publications 2024: 2 publications 2025: 17 publications
1988 2025

914 publications in total across all disciplines

View publications per year as a table
J. A. Tenreiro Machado: publications per year, 1988 to 2025
Year Publications
1988 7
1989 1
1990 6
1991 6
1992 1
1993 5
1994 1
1995 2
1996 1
1997 12
1998 11
1999 5
2000 10
2001 6
2002 8
2003 11
2004 25
2005 15
2006 29
2007 32
2008 28
2009 41
2010 34
2011 50
2012 35
2013 55
2014 37
2015 44
2016 47
2017 50
2018 41
2019 72
2020 69
2021 66
2022 30
2023 2
2024 2
2025 17
Total 914
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J. A. Tenreiro Machado publications per year - data summary

  • J. A. Tenreiro Machado, a Mathematics scholar from Polytechnic Institute of Porto, has 914 publications recorded across 38 years, from 1988 to 2025.
  • The oldest publication on record dates to 1988 and the most recent to 2025.
  • The most productive year is 2019, with 72 publications.
  • The least productive years with any output are 1989, 1992, 1994 and 1996, with 1 publication each.
  • The rate of publication averages 24.1 papers per year over the whole span, or 24.1 per year counting only the 38 years with at least one publication.
  • The last 5 years on the chart (2021-2025) hold 117 publications, 13% of the career total.
  • Split into equal eras - 1988-2000: 68 publications (5.2 per year); 2001-2013: 369 publications (28.4 per year); 2014-2025: 477 publications (39.8 per year).
  • Comparing the opening and closing eras, the overall trend of publication is rising.

J. A. Tenreiro Machado publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where J. A. Tenreiro Machado sits on this spectrum.

No. of scientists
25 50 75 100
Bar chart with 100 bars. Horizontal axis: publications, 42–46 to 537+. Vertical axis: number of scientists, 0 to 112. Most scientists, 112, have 142–146 publications. The last bar groups every scientist with 537 publications or more. The highlighted bar, 537+ publications, is where this scientist sits. 42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientist 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientist 522–526 publications: 3 scientists 527–531 publications: 1 scientist 532–536 publications: 4 scientists 537+ publications: 100 scientists
42–46 publications 537+

This scientist: 786 publications — 99th percentile

99% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

View publications distribution as a table
Number of Mathematics scientists by publication count, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
Publications Scientists This scientist
42–46 3
47–51 5
52–56 7
57–61 20
62–66 14
67–71 25
72–76 19
77–81 35
82–86 50
87–91 60
92–96 86
97–101 84
102–106 83
107–111 90
112–116 99
117–121 90
122–126 91
127–131 109
132–136 110
137–141 98
142–146 112
147–151 102
152–156 88
157–161 106
162–166 83
167–171 102
172–176 77
177–181 81
182–186 78
187–191 71
192–196 92
197–201 64
202–206 69
207–211 64
212–216 62
217–221 58
222–226 53
227–231 50
232–236 46
237–241 46
242–246 46
247–251 43
252–256 29
257–261 45
262–266 30
267–271 33
272–276 34
277–281 30
282–286 31
287–291 21
292–296 34
297–301 26
302–306 10
307–311 17
312–316 23
317–321 13
322–326 16
327–331 26
332–336 13
337–341 13
342–346 16
347–351 17
352–356 12
357–361 18
362–366 18
367–371 9
372–376 11
377–381 8
382–386 8
387–391 9
392–396 9
397–401 8
402–406 11
407–411 6
412–416 6
417–421 9
422–426 8
427–431 5
432–436 8
437–441 8
442–446 4
447–451 4
452–456 4
457–461 2
462–466 2
467–471 4
472–476 3
477–481 3
482–486 6
487–491 3
492–496 5
497–501 5
502–506 1
507–511 6
512–516 4
517–521 1
522–526 3
527–531 1
532–536 4
537+ 100 786
Download as CSV

J. A. Tenreiro Machado publication distribution in Mathematics in 2026 - data summary

  • The chart plots the publication count of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 100 ranges running from 42–46 to 537+ publications.
  • J. A. Tenreiro Machado, a Mathematics scholar from Polytechnic Institute of Porto, records 786 publications - the 99th percentile of the discipline.
  • 99% of ranked Mathematics scientists score the same or lower than J. A. Tenreiro Machado, and about 1% score higher.
  • The median of the discipline falls in the 172–176 publications range, and J. A. Tenreiro Machado ranks above the median.
  • The most crowded range is 142–146 publications, holding 112 scientists (3% of the field).
  • 47% of the field sits in the lowest quarter of the value range (up to 162–166 publications), so the distribution leans towards the lower end of the scale.
  • The final bar has no upper bound: it groups every scientist with 537 publications or more, 100 scientists in all (3% of the field).

J. A. Tenreiro Machado D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where J. A. Tenreiro Machado sits on this spectrum.

No. of scientists
50 100 150
Bar chart with 57 bars. Horizontal axis: D-Index, 30 to 86+. Vertical axis: number of scientists, 0 to 174. Most scientists, 174, have 30 D-Index. The last bar groups every scientist with 86 D-Index or more. The highlighted bar, 86+ D-Index, is where this scientist sits. 30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 89 D-Index — 98th percentile

98% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

View D-Index distribution as a table
Number of Mathematics scientists by D-index, Research.com 2026 ranking edition. Based on 3,584 ranked scientists.
D-Index Scientists This scientist
30 174
31 151
32 174
33 117
34 136
35 127
36 145
37 153
38 150
39 150
40 138
41 136
42 93
43 108
44 115
45 112
46 103
47 75
48 59
49 67
50 60
51 57
52 59
53 62
54 60
55 50
56 42
57 54
58 50
59 42
60 41
61 35
62 40
63 21
64 31
65 27
66 29
67 19
68 25
69 17
70 18
71 12
72 14
73 13
74 18
75 9
76 11
77 10
78 9
79 16
80 12
81 10
82 5
83 5
84 13
85 6
86+ 99 89
Download as CSV

J. A. Tenreiro Machado D-index placement in Mathematics in 2026 - data summary

  • The chart plots the discipline H-index (D-index) of all 3,584 Mathematics scientists ranked by Research.com in 2026, grouped into 57 ranges running from 30 to 86+ D-Index.
  • J. A. Tenreiro Machado, a Mathematics scholar from Polytechnic Institute of Porto, records 89 D-Index - the 98th percentile of the discipline.
  • 98% of ranked Mathematics scientists score the same or lower than J. A. Tenreiro Machado, and about 2% score higher.
  • The median of the discipline falls in the 42 D-Index range, and J. A. Tenreiro Machado ranks above the median.
  • The most crowded range is 30 D-Index, holding 174 scientists (5% of the field).
  • 58% of the field sits in the lowest quarter of the value range (up to 44 D-Index), so the distribution is heavily right-skewed and high scores are rare.
  • The final bar has no upper bound: it groups every scientist with 86 D-Index or more, 99 scientists in all (3% of the field).

Research.com Recognitions

  • 2026 - Research.com Electronics and Electrical Engineering in Portugal Leader Award
  • 2026 - Research.com Mathematics in Portugal Leader Award
  • 2025 - Research.com Electronics and Electrical Engineering in Portugal Leader Award
  • 2025 - Research.com Mathematics in Portugal Leader Award
  • 2022 - Research.com Engineering and Technology in Portugal Leader Award

Overview

J. A. Tenreiro Machado is affiliated with the Polytechnic Institute of Porto in Portugal and has a significant body of research contributions primarily in the fields of Mathematics and Engineering. Their work covers numerous subfields including Modeling and Simulation, Control and Systems Engineering, Numerical Analysis, Statistical and Nonlinear Physics, and Mechanics of Materials.

The main topics addressed in their research focus on Fractional Differential Equations Solutions, Advanced Control Systems Design, Iterative Methods for Nonlinear Equations, Numerical methods in engineering, Differential Equations and Numerical Methods, Chaos control and synchronization, and Complex Systems and Time Series Analysis.

Tenreiro Machado has published recent papers such as:

  • "Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method" (2020) in Physica Scripta
  • "Trends, directions for further research, and some open problems of fractional calculus" (2022) in Nonlinear Dynamics
  • "The recovery of global stock markets indices after impacts due to pandemics" (2020) in Research in International Business and Finance
  • "Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems" (2020) in Applied Mathematical Modelling
  • "A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations" (2020) in Frontiers of Information Technology & Electronic Engineering

Frequent coauthors collaborating with Tenreiro Machado include António M. Lopes, Z. Avazzadeh, O. Nikan, Hossein Hassani, and Alireza Alfi.

The scientist has contributed extensively to several publication venues, with the most frequent being Mathematics, Nonlinear Dynamics, Applied Mathematical Modelling, Communications in Nonlinear Science and Numerical Simulation, and Mathematical Methods in the Applied Sciences.

Regarding book publications, Tenreiro Machado has contributed to titles released by Springer Nature and Springer International Publishing, including:

  • "Advances in Design, Simulation and Manufacturing IV" (2021)
  • "Innovations in Industrial Engineering II" (2022)
  • "Advances in Manufacturing III" (2022)
  • "Mathematical Topics on Modelling Complex Systems" (2022)
  • "Numerical Solutions of Realistic Nonlinear Phenomena" (2020)
  • "Mathematical Methods in Modern Complexity Science" (2022)
  • "Advances in Nonlinear Dynamics" (2022)

Best Publications

  • Advances in Fractional Calculus

    Jocelyn Sabatier;Om Prakash Agrawal;J. A. Tenreiro Machado

  • Recent history of fractional calculus

    J. A. Tenreiro Machado;Virginia Kiryakova;Francesco Mainardi

  • Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering

    J. Sabatier;O. P. Agrawal;J. A. Tenreiro Machado

  • Fractional Dynamics and Control

    Dumitru Baleanu;Jos Antnio Tenreiro Machado;Albert C. J. Luo

  • New Trends in Nanotechnology and Fractional Calculus Applications

    Dumitru Baleanu;Ziya B. Guvenc;J. A. Tenreiro Machado

  • The role of fractional calculus in modeling biological phenomena: A review

    Clara-Mihaela Ionescu;A. Lopes;Dana Copot;J. A. T. Machado

  • A Review of Definitions for Fractional Derivatives and Integral

    Edmundo Capelas de Oliveira;José António Tenreiro Machado

  • Towards the development of intelligent transportation systems

    L. Figueiredo;I. Jesus;J.A.T. Machado;J.R. Ferreira

  • What is a fractional derivative

    Manuel D. Ortigueira;J.A. Tenreiro Machado

  • Analysis and design of fractional-order digital control systems

    J. A. Tenreiro Machado

  • A review of definitions of fractional derivatives and other operators

    G. Sales Teodoro;J.A. Tenreiro Machado;E. Capelas de Oliveira

  • Some Applications of Fractional Calculus in Engineering

    J. A. Tenreiro Machado;Manuel F. Silva;Ramiro S. Barbosa;Isabel S. Jesus

  • Tuning of PID Controllers Based on Bode's Ideal Transfer Function

    Ramiro S. Barbosa;J. A. Tenreiro Machado;Isabel M. Ferreira

  • Fractional Order Calculus: Basic Concepts and Engineering Applications

    Ricardo Enrique Gutiérrez;João Maurício Rosário;José Tenreiro Machado

  • Discrete-time fractional-order controllers

    J. A. Tenreiro Machado

  • A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow

    Xiao-Jun Yang;Hari M. Srivastava;J. A. Tenreiro Machado

  • Development of fractional order capacitors based on electrolyte processes

    Isabel S. Jesus;J. A. Tenreiro Machado

  • Particle swarm optimization with fractional-order velocity

    E. J. Solteiro Pires;J. A. Tenreiro Machado;P. B. de Moura Oliveira;J. Boaventura Cunha

  • A new fractional operator of variable order: Application in the description of anomalous diffusion

    Xiao-Jun Yang;J.A. Tenreiro Machado

  • On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

    Xiao-Jun Yang;J. A. Tenreiro Machado;Dumitru Baleanu;Carlo Cattani

Frequent Co-Authors

António M. Lopes
António M. Lopes University of Porto
Manuel Silva
Manuel Silva University of Zaragoza
Dumitru Baleanu
Dumitru Baleanu Lebanese American University
Xiao-Jun Yang
Xiao-Jun Yang China University of Mining and Technology
Manuel Duarte Ortigueira
Manuel Duarte Ortigueira Universidade Nova de Lisboa
Alireza Alfi
Alireza Alfi Shahrood University of Technology
Imre J. Rudas
Imre J. Rudas Óbuda University
Hari M. Srivastava
Hari M. Srivastava University of Victoria
Carlo Cattani
Carlo Cattani Tuscia University
Mahmoud A. Zaky
Mahmoud A. Zaky National Research Centre, Egypt

External Links

Personal website of J. A. Tenreiro Machado Google Scholar page

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