We show how a rescaling of fractional operators with bounded kernels may help circumvent
their documented deficiencies, for example, the inconsistency at zero or the lack of inverse …

We develop a theory on linear L-fractional differential equations. The L-fractional derivative
${}^ L\! D^\alpha $ is defined as a certain normalization of the well-known Caputo derivative …

The physical interpretation of a variable-order fractional diffusion equation within the
framework of the multiple trapping model is presented. This interpretation enables the …

A generalization of fractional linear viscoelasticity based on Scarpi's approach to variable-
order fractional calculus is presented. After reviewing the general mathematical framework …

We investigate a semilinear problem for a fractional diffusion equation with variable order
Caputo fractional derivative∂ t β (t) u (t) subject to homogeneous Dirichlet boundary …

This paper explores a general class of singular kernels with the objective of designing new
families of uniformly continuous sliding mode controllers. The proposed controller results …

In this article we solve the Cauchy problem for the relaxation equation posed in a framework
of variable order fractional calculus. Thus, we solve the relaxation equation in, what seems …

Recently, a different approach to define fractional-order operators of variable order has been
proposed and investigate [1]. Unlike other operators, this approach is based on the …