INdAM workshop on Fractional Differential Equations:
Modeling, Discretization, and Numerical Solvers
The INdAM workshop “Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers” will take place in Rome, July 12-14, 2021 and partially online.
The in presence part of the workshop will take place at Best Western Globus Hotel in Viale Ippocrate, 119, 00161, Roma (RM), inside the Ping room.
Fractional calculus deals with the study and application of integrals and derivatives of non-integer order. These operators, unlike the classic operators of integer order, are non-local operators and are better suited to describe phenomena with memory (with respect to time and/or space).
Although the basic ideas of fractional calculus go back over three centuries, only in recent decades has there been a rapid increase in interest towards this field of research, due not only to the increasing use fractional calculus in applications in biology, physics, engineering, probability, etc., but also thanks to the availability of new and more powerful numerical tools that allows for an efficient solution of problems that until a few years ago appeared unsolvable.
In fact, numerical analysis plays a decisive role in fractional calculus. The analytical solution of fractional differential equations (FDEs) appears even more difficult than in the integer case and, therefore, practically every type of application of fractional calculus requires adequate numerical tools.
This workshop, therefore, aims to bring together the two communities of numerical analysts operating in this field – the ones working on methods for the solution of differential problems and the one working on the numerical linear algebra side – to share knowledge and create synergies. It also intends to encourage meetings with researchers who deal with these problems from a more applicative point of view, both in fields such as mathematical physics and in fields with an higher technological content such as image recognition and engineering (especially in the automatic control of systems).
The main topics of the workshop are:
- Numerical methods for differential problems of fractional order
- Solving systems of large linear equations with dense matrices and use of preconditioners
- Fractional Laplacian
- Image processing using fractional operators
- Application in physics of fractional operators
- Machine learning techniques in the fractional environment