The Mittag-Leffler (ML) function plays a fundamental role in fractional calculus but very few
methods are available for its numerical evaluation. In this work we present a method for the …

Exponential Euler discrete schemes have been widely employed in the studies of Caputo
fractional order differential equations, but almost no literature concerns the Caputo–Fabrizio …

Solving differential equations of fractional (ie, non-integer) order in an accurate, reliable and
efficient way is much more difficult than in the standard integer-order case; moreover, the …

Particle-laden flows are ubiquitous, ranging across systems such as platelets in blood, dust
storms, marine snow, and cloud droplets. The dynamics of a small particle in such non …

COVID-19 pandemic has impacted people all across the world. As a result, there has been a
collective effort to monitor, predict, and control the spread of this disease. Among this effort is …

We present a survey of fractional differential equations and in particular of the computational
cost for their numerical solutions from the view of computer science. The computational …

The time-fractional Schrödinger equation is a fundamental topic in physics and its numerical
solution is still an open problem. Here we start from the possibility to express its solution by …

This paper addresses the problem of the numerical computation of generalized Mittag–
Leffler functions with two parameters, with applications in fractional calculus. The inversion …

A fourth-order implicit-explicit time-discretization scheme based on the exponential time
differencing approach with a fourth-order compact scheme in space is proposed for space …

Forecasting water content dynamics in heterogeneous porous media has significant interest
in hydrological applications; in particular, the treatment of infiltration when in presence of …