What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Fractional calculus (39.78%)
- Mathematical analysis (36.86%)
- Random walk (17.15%)
What were the highlights of his more recent work (between 2016-2021)?
- Fractional calculus (39.78%)
- Function (11.68%)
- Mathematical analysis (36.86%)
In recent papers he was focusing on the following fields of study:
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.
Between 2016 and 2021, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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