The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

We present a collection of recent results on the numerical approximation of Volterra integral
equations and integro-differential equations by means of collocation type methods, which …

In this work we employ integer-and fractional-order viscoelastic models in a one-
dimensional blood flow solver, and study their behavior by presenting an in-silico study on a …

In this paper, we propose a fast algorithm for the variable-order (VO) Caputo fractional
derivative based on a shifted binary block partition and uniform polynomial approximations …

A unified fast time-stepping method for both fractional integral and derivative operators is
proposed. The fractional operator is decomposed into a local part with memory …

The nonlocal nature of the fractional integral makes the numerical treatment of fractional
differential equations expensive in terms of computational effort and memory requirements …

We develop efficient numerical methods for fractional order PDEs, and employ them to
investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations …

The solution of fractional-order differential problems requires in the majority of cases the use
of some computational approach. In general, the numerical treatment of fractional differential …

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO
function α (t) ∈ (0, 1) α (t)∈(0, 1), we develop an exponential-sum-approximation (ESA) …

In this work, we extend the fractional linear multistep methods in C. Lubich, SIAM J. Math.
Anal., 17 (1986), pp. 704--719 to the tempered fractional integral and derivative operators in …