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Mathematics
Italy
2026

D-Index & Metrics

Mathematics

D-Index
72
Citations
32172
World Ranking
240
National Ranking
5

Francesco Mainardi 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 Francesco Mainardi sits on this spectrum.

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 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 223 publications — 70th percentile

70% of scientists in this discipline score the same or lower.

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

Francesco Mainardi 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 Francesco Mainardi sits on this spectrum.

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: 72 D-Index — 93rd percentile

93% of scientists in this discipline score the same or lower.

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

Research.com Recognitions

  • 2026 - Research.com Mathematics in Italy Leader Award
  • 2025 - Research.com Mathematics in Italy Leader Award
  • 2023 - Research.com Mathematics in Italy Leader Award
  • 2022 - Research.com Mathematics in Italy Leader Award

Overview

Francesco Mainardi is affiliated with the National Institute for Nuclear Physics in Italy and has contributed extensively to the field of mathematics, with a particular focus on applied mathematics and fractional calculus. The body of research includes work on fractional differential equations, mathematical functions, and nonlinear equations, as well as applications in mechanics and biomedical engineering.

The main fields of study for this researcher include:

  • Mathematics

Within this broad domain, the subfields of study covered are:

  • Applied Mathematics
  • Modeling and Simulation
  • Numerical Analysis
  • Mechanics of Materials
  • Biomedical Engineering

Key topics of research focused on by Francesco Mainardi are:

  • Fractional Differential Equations Solutions
  • Mathematical functions and polynomials
  • Iterative Methods for Nonlinear Equations
  • Nonlinear Differential Equations Analysis
  • Thermoelastic and Magnetoelastic Phenomena
  • Numerical methods in engineering
  • Composite Structure Analysis and Optimization

The researcher has coauthored papers frequently with several scholars, including:

  • Sergei Rogosin
  • Rudolf Gorenflo
  • Anatoly A. Kilbas
  • Roberto Garra
  • Filippo Giraldi

Francesco Mainardi's recent published papers include:

  • "A Practical Guide to Prabhakar Fractional Calculus" (2020), published in Fractional Calculus and Applied Analysis
  • "Variable-order fractional calculus: A change of perspective" (2021), published in Communications in Nonlinear Science and Numerical Simulation
  • "On the Advent of Fractional Calculus in Econophysics via Continuous-Time Random Walk" (2020), published in Mathematics
  • "Thermoelasticity and P-wave simulation based on the Cole-Cole model" (2020), published in Journal of Thermal Stresses
  • "Some applications of wright functions in fractional differential equations" (2021), published in Reports on Mathematical Physics

The most frequent publication venues where the researcher has contributed are:

  • Mathematics
  • arXiv (Cornell University)
  • Fractional Calculus and Applied Analysis
  • Symmetry
  • Surveys in Geophysics

In terms of book publications, Francesco Mainardi has authored work published by Springer Science+Business Media, including the book "Mittag-Leffler Functions, Related Topics and Applications" (2020).

Best Publications

  • Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models

    Francesco Mainardi

  • Recent history of fractional calculus

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

  • Fractional Calculus: Integral and Differential Equations of Fractional Order

    Rudolf Gorenflo;Francesco Mainardi

  • Mittag-Leffler Functions, Related Topics and Applications

    Rudolf Gorenflo;Anatoly A. Kilbas;Francesco Mainardi;Sergei V. Rogosin

  • Fractals and fractional calculus in continuum mechanics

    Alberto Carpinteri;F. Mainardi

  • Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics

    Francesco Mainardi

  • Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena

    Francesco Mainardi

  • Multi-index Mittag-Leffler Functions

    Rudolf Gorenflo;Anatoly A. Kilbas;Francesco Mainardi;Sergei V. Rogosin

  • A new dissipation model based on memory mechanism

    M. Caputo;F. Mainardi

  • Fractional calculus and continuous-time finance

    Enrico Scalas;Rudolf Gorenflo;Francesco Mainardi

  • Linear models of dissipation in anelastic solids

    M. Caputo;F. Mainardi

  • The fundamental solution of the space-time fractional diffusion equation

    Francesco Mainardi;Yuri Luchko;Gianni Pagnini

  • The fundamental solutions for the fractional diffusion-wave equation

    F. Mainardi

  • On Mittag-Leffler-type functions in fractional evolution processes

    Francesco Mainardi;Rudolf Gorenflo

  • Fractional calculus and continuous-time finance II: the waiting- time distribution

    Francesco Mainardi;Marco Raberto;Rudolf Gorenflo;Enrico Scalas

  • Waiting-times and returns in high-frequency financial data: an empirical study

    Marco Raberto;Enrico Scalas;Francesco Mainardi

  • Creep, relaxation and viscosity properties for basic fractional models in rheology

    F. Mainardi;G. Spada

  • Time Fractional Diffusion: A Discrete Random Walk Approach

    Rudolf Gorenflo;Francesco Mainardi;Daniele Moretti;Paolo Paradisi

  • Discrete random walk models for space-time fractional diffusion

    Rudolf Gorenflo;Francesco Mainardi;Daniele Moretti;Gianni Pagnini

  • Wright functions as scale-invariant solutions of the diffusion-wave equation

    Rudolf Gorenflo;Yuri Luchko;Francesco Mainardi

Frequent Co-Authors

Rudolf Gorenflo
Rudolf Gorenflo Freie Universität Berlin
Marco Raberto
Marco Raberto University of Genoa
Anatoly A. Kilbas
Anatoly A. Kilbas Belarusian State University
Yuri Luchko
Yuri Luchko Beuth University of Applied Sciences
J. A. Tenreiro Machado
J. A. Tenreiro Machado Polytechnic Institute of Porto
Giorgio Spada
Giorgio Spada University of Bologna
Gérard A. Maugin
Gérard A. Maugin Sorbonne University
Alberto Carpinteri
Alberto Carpinteri Shantou University
Boris A. Malomed
Boris A. Malomed Tel Aviv University

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