This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

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 …

The paper describes different approaches to generalize the trapezoidal method to fractional
differential equations. We analyze the main theoretical properties and we discuss …

Fractional finite difference methods are useful to solve the fractional differential equations.
The aim of this article is to prove the stability and convergence of the fractional Euler …

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some
applications in fractional calculus, are discussed. In general the evaluation of a scalar …

Numerical solution of hyperbolic partial differential equation with an integral condition
continues to be a major research area with widespread applications in modern physics and …

Many physical phenomena are modeled by nonclassical parabolic boundary value
problems with nonlocal boundary conditions. In place of the classical specification of …

Certain problems arising in engineering are modeled by nonstandard parabolic initial‐
boundary value problems in one space variable, which involve an integral term over the …

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 …

We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear
fractional differential equations with fractional order 0<β<1. From the known structure of the …