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 …

New variable-order fractional chaotic systems are proposed in this paper. A concept of short
memory is introduced where the initial point in the Caputo derivative is varied. The fractional …

A novel fractional model based on the Riemann Liouville fractional derivative to simulate the
thermal performance of conventional solar still and show the effect of using hybrid nanofluid …

This paper studies the design of variable-order fractional proportional–integral–derivative
(VFPID) controllers for linear dynamical systems. For this purpose, a technique to discretize …

An accurate characterization of rocks for the modelling of creep is an essential step toward
ensuring the safety with respect to reliability of underground rock engineering. In this work, a …

Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

Multi-term variable-order fractional differential equations (VO-FDEs) are considered to be
one of the tools to illustrate the behavior of transient-regime real-life phenomena precisely …

In this paper, we propose a fast algorithm for the variable-order (VO) Caputo fractional
derivative based on a shifted binary block partition and uniform polynomial approximations …

A special point on each time interval is found for the approximation of the variable-order time
Caputo derivative, which makes at least second order approximation accuracy be obtained …