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 …

In this paper, we will first present the TFMIADM with its adequate Dirichlet constraints. Right
after that, we will review the formation of that model under the terms and assumptions of the …

Current discretizations of variable-order fractional (V-OF) differential equations lead to
numerical solutions of low order of accuracy. This paper explores a high order numerical …

While several high-order methods have been developed for fractional PDEs (FPDEs) with
fixed order, there are no such methods for FPDEs with field-variable order. These equations …

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 …

When considering the price change of the underlying fractal transmission system, a
fractional Black–Scholes (BS) model with an α-order time fractional derivative is derived. In …

We investigate the potential of fractional order operators to develop accurate and efficient
models for acoustic black hole (ABH) terminations in ducts. While previous research has …

A water–air triboelectric nanogenerator (WATENG) is presented for CO2 sensing
application. During the operation of WATENG, two independent charge transfers can be …

This paper reports a novel numerical technique for solving the time variable fractional order
mobile-immobile advection-dispersion (TVFO-MIAD) model with the Coimbra variable time …