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- Francesco Mainardi

Mathematics

Italy

2023

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
68
Citations
27,254
206
World Ranking
220
National Ranking
5

2023 - Research.com Mathematics in Italy Leader Award

2022 - Research.com Mathematics in Italy Leader Award

- Mathematical analysis
- Statistics
- Algebra

Francesco Mainardi mainly investigates Fractional calculus, Mathematical analysis, Random walk, Diffusion equation and Time derivative. His Fractional calculus study incorporates themes from Probability density function and Calculus. The Mathematical analysis study which covers Anomalous diffusion that intersects with Heterogeneous random walk in one dimension.

Francesco Mainardi works mostly in the field of Random walk, limiting it down to topics relating to Stochastic process and, in certain cases, Statistical finance and Econophysics, as a part of the same area of interest. His studies in Time derivative integrate themes in fields like Mathematical physics, Continuum, Auxiliary function, Brownian motion and Continuum mechanics. The concepts of his Differential equation study are interwoven with issues in Fractal, Time-scale calculus and Fourier integral operator.

- Fractals and fractional calculus in continuum mechanics (1017 citations)
- Recent history of fractional calculus (908 citations)
- Fractional Calculus: Integral and Differential Equations of Fractional Order (875 citations)

Francesco Mainardi mainly focuses on Fractional calculus, Mathematical analysis, Random walk, Diffusion equation and Applied mathematics. His research in Fractional calculus is mostly concerned with Mittag-Leffler function. His studies deal with areas such as Anomalous diffusion and Viscoelasticity as well as Mathematical analysis.

His Random walk study combines topics in areas such as Financial market, Statistical finance and Random variable. His work in Diffusion equation addresses issues such as Wave equation, which are connected to fields such as Constant. His Applied mathematics research incorporates elements of Initial value problem, Renewal theory and Integral equation.

- Fractional calculus (39.78%)
- Mathematical analysis (36.86%)
- Random walk (17.15%)

- Fractional calculus (39.78%)
- Function (11.68%)
- Mathematical analysis (36.86%)

Francesco Mainardi spends much of his time researching Fractional calculus, Function, Mathematical analysis, Applied mathematics and Laplace transform. His research integrates issues of Initial value problem, Stochastic process, Diffusion equation, Dirac delta function and Calculus in his study of Fractional calculus. His biological study spans a wide range of topics, including Poisson distribution, Generalization, Exponential function and Relaxation.

Francesco Mainardi has included themes like Dispersion relation, Korteweg–de Vries equation, Wave propagation, Phase velocity and Viscoelasticity in his Mathematical analysis study. His Applied mathematics research integrates issues from Index and Partial differential equation. His Laplace transform research includes elements of Type, Simple, Thermal conduction, Power series and Series.

- A practical guide to Prabhakar fractional calculus (37 citations)
- A class of linear viscoelastic models based on Bessel functions (36 citations)
- On the propagation of transient waves in a viscoelastic Bessel medium (29 citations)

- Mathematical analysis
- Statistics
- Algebra

Francesco Mainardi focuses on Fractional calculus, Viscoelasticity, Function, Mathematical analysis and Laplace transform. Francesco Mainardi has researched Fractional calculus in several fields, including Transcendental number, Stochastic process, Differential equation, Generalization and Calculus. His study looks at the relationship between Viscoelasticity and fields such as Volterra integral equation, as well as how they intersect with chemical problems.

His Function research is multidisciplinary, incorporating perspectives in Applied mathematics, Diffusion equation and Relaxation. His primary area of study in Mathematical analysis is in the field of Bessel function. In his work, Wright Omega function, Anomalous diffusion and Analytic continuation is strongly intertwined with Special functions, which is a subfield of Laplace transform.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

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

Francesco Mainardi.

**(2010)**

2755 Citations

Fractional Calculus: Integral and Differential Equations of Fractional Order

Rudolf Gorenflo;Francesco Mainardi.

arXiv: Mathematical Physics **(2008)**

1455 Citations

Recent history of fractional calculus

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

Communications in Nonlinear Science and Numerical Simulation **(2011)**

1430 Citations

Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics

Francesco Mainardi.

arXiv: Statistical Mechanics **(2001)**

1237 Citations

Mittag-Leffler Functions, Related Topics and Applications

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

**(2014)**

1217 Citations

Multi-index Mittag-Leffler Functions

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

**(2014)**

1210 Citations

Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena

Francesco Mainardi.

Chaos Solitons & Fractals **(1996)**

1105 Citations

Fractals and fractional calculus in continuum mechanics

Alberto Carpinteri;F. Mainardi.

**(1997)**

1086 Citations

The fundamental solution of the space-time fractional diffusion equation

Francesco Mainardi;Yuri Luchko;Gianni Pagnini.

arXiv: Statistical Mechanics **(2007)**

901 Citations

Linear models of dissipation in anelastic solids

M. Caputo;F. Mainardi.

La Rivista del Nuovo Cimento (1971-1977) **(1971)**

887 Citations

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