Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other
variables dependent order have been successfully applied to investigate time and/or space …

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

Classic Newtonian mechanics assumes that space and time are continuous everywhere.
The basic physical quantities (eg speed, acceleration and force) can be described by an …

This book contains mathematical preliminaries in which basic definitions of fractional
derivatives and spaces are presented. The central part of the book contains various …

The purpose of this paper is to offer a unified discussion of variable-order differential
operators in anomalous diffusion modeling. The characteristics of the new models, in …

How to characterize the memory property of systems is a challenging issue in the modeling
and analysis of complex systems. This study makes a comparative investigation of integer …

The cable equation plays a central role in many areas of electrophysiology and in modeling
neuronal dynamics. This paper reports an accurate spectral collocation method for solving …

Fractional calculus allows variable-order of fractional operators, which can be exploited in
diverse physical and biological applications where rates of change of the quantity of interest …

In this paper, we consider a variable-order anomalous subdiffusion equation. A numerical
scheme with first order temporal accuracy and fourth order spatial accuracy for the equation …

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion
Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation …