2026 Francesco Mainardi: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	72	240	203	5	5	223	32172

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

2962
Citations
Recent history of fractional calculus

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

1821
Citations
Fractional Calculus: Integral and Differential Equations of Fractional Order

Rudolf Gorenflo;Francesco Mainardi

1581
Citations
Mittag-Leffler Functions, Related Topics and Applications

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

1561
Citations
Fractals and fractional calculus in continuum mechanics

Alberto Carpinteri;F. Mainardi

1373
Citations
Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics

Francesco Mainardi

1296
Citations
Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena

Francesco Mainardi

1249
Citations
Multi-index Mittag-Leffler Functions

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

1241
Citations
A new dissipation model based on memory mechanism

M. Caputo;F. Mainardi

1032
Citations
Fractional calculus and continuous-time finance

Enrico Scalas;Rudolf Gorenflo;Francesco Mainardi

1021
Citations
Linear models of dissipation in anelastic solids

M. Caputo;F. Mainardi

1016
Citations
The fundamental solution of the space-time fractional diffusion equation

Francesco Mainardi;Yuri Luchko;Gianni Pagnini

985
Citations
The fundamental solutions for the fractional diffusion-wave equation

F. Mainardi

846
Citations
On Mittag-Leffler-type functions in fractional evolution processes

Francesco Mainardi;Rudolf Gorenflo

665
Citations
Fractional calculus and continuous-time finance II: the waiting- time distribution

Francesco Mainardi;Marco Raberto;Rudolf Gorenflo;Enrico Scalas

656
Citations
Waiting-times and returns in high-frequency financial data: an empirical study

Marco Raberto;Enrico Scalas;Francesco Mainardi

591
Citations
Creep, relaxation and viscosity properties for basic fractional models in rheology

F. Mainardi;G. Spada

574
Citations
Time Fractional Diffusion: A Discrete Random Walk Approach

Rudolf Gorenflo;Francesco Mainardi;Daniele Moretti;Paolo Paradisi

474
Citations
Discrete random walk models for space-time fractional diffusion

Rudolf Gorenflo;Francesco Mainardi;Daniele Moretti;Gianni Pagnini

396
Citations
Wright functions as scale-invariant solutions of the diffusion-wave equation

Rudolf Gorenflo;Yuri Luchko;Francesco Mainardi

381
Citations

Frequent Co-Authors

Rudolf Gorenflo Freie Universität Berlin

Marco Raberto University of Genoa

Anatoly A. Kilbas Belarusian State University

Yuri Luchko Beuth University of Applied Sciences

J. A. Tenreiro Machado Polytechnic Institute of Porto

Giorgio Spada University of Bologna

Gianaurelio Cuniberti TU Dresden

Alberto Carpinteri Shantou University

Boris A. Malomed Tel Aviv University

Thomas J. Royston University of Illinois at Chicago

External Links

Wikipedia of Francesco Mainardi Personal website of Francesco Mainardi Google Scholar page

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