# Functional Analysis, Approximation Theory and Numerical Analysis

## Matera, Italy, July 5-8, 2022

**Session:** **Recent Advances in the Analysis and Numerical Solution of Evolutionary Integral Equations**

Due to their ability to capture memory effects, integral and
integro-differential equations of
Volterra type describe a wide variety
of dynamic processes that depend on the past history of the
system. The
effective impact of these models is evident in literature where
analytical and numerical
studies have, in recent years, led to a deeper
understanding of many applications in the real world.
Indeed, there have
been very significant advances in the theory, applications and
qualitative properties
of both continuous and discrete solutions as well
as in the development of numerically efficient
methods. In this
session, recognized researchers in the area of Volterra integral and
related
equations will present their recent achievements and discuss
possible future developments.

**Organizers:**

- Dajana Conte,
*dajconte@unisa.it*
- Teresa Diogo,
*tdiogo@math.ist.utl.pt*
- Eleonora Messina,
*eleonora.messina@unina.it*

**Talks:**

- L. Aceto,
*On the computation of the Wright function and its
applications to Fractional Calculus*
- J.A.D. Appleby,
*Characterisation of the asymptotic behaviour of the
mean-square of linear stochastic Volterra equations*
- M.I. Berenguer,
*Approximating the
fixed point of an affine operator*
- I.M. Bulai,
*Modeling metastatic tumor evolution, numerical
resolution and growth prediction*
- A. Cardone,
*Highly accurate solution of fractional
differential equations*
- E. Cuesta,
*A posteriori error estimates for time discretization
of abstract semi-linear fractional integro-differential equations*
- R. Garrappa,
*Efficient computation of solutions of time-fractional
difusion-reaction equations*
- K. Lätt,
*Numerical schemes for a class of
singular fractional integro-differential equations*
- E. Lawless,
*Real exponential asymptotic
behaviour is generic in the mean square of two-dimensional linear SDE's*
- H. Liang,
*A general collocation analysis for weakly singular
Volterra integral equations with variable exponent*
- S. Micula,
*A Numerical Method for Volterra-Fredholm
Integral Equations in Two Dimensions*
- L. Moradi,
*Numerical solution of delay Volterra functional
integral equations with variable bounds*
- E. Sousa,
*On the convergence of difference approximations to
fractional differential problems in bounded domains*
- M. Vikerpuur,
*Central part interpolation schemes for fractional
differential equations*