Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

We present a new numerical tool to solve partial differential equations involving Caputo
derivatives of fractional variable order. Three Caputo-type fractional operators are …

Fractional Calculus had a remarkable evolution during recent decades, and paved the way
towards the definition of variable order derivatives. In the literature we find several different …

This is a tutorial study to introduce fractional control to a reader with a background in control
theory. Fractional controllers are those making use of fractional-order derivatives and …

Due to the non-idealities of commercial inductors, the demand for a better model that
accurately describe their dynamic response is elevated. So, the fractional order models of …

In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC)
is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic …

The book illustrates the theoretical results of fractional derivatives via applications in signals
and systems, covering continuous and discrete derivatives, and the corresponding linear …

An adaptive fuzzy fractional order sliding mode control (FFOSMC) is introduced for a high
performance servo actuation system that is subjected to aerodynamic loads and …

The twentieth century was rich in great scientific discoveries. One of the most influential
events is the introduction of diffusion process, which has been widely used in physics …

In this paper, we present the ψ ψ-Hilfer fractional derivatives of variable order (FDVO) of 3
types I, II and III, versions A and B, as well as their combinations. In addition, we propose …