### 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.

#### The workshop

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 there has 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 one 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