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 …

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 …

Accurate Li-ion battery modeling is integral to the design of effective battery management
systems in electric vehicles. However, the voltage–current (U–I) characteristic of Li-ion …

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 …

The aim of this paper is to develop an accurate discretization technique to solve a class of
variable-order fractional (VOF) reaction-diffusion problems. In the spatial direction, the …

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 …

This paper is about to formulate a design of predator–prey model with constant and time
fractional variable order. The predator and prey act as agents in an ecosystem in this …

In this study a new framework for solving three-dimensional (3D) time fractional diffusion
equation with variable-order derivatives is presented. Firstly, a θ-weighted finite difference …

We generalize existing Jacobi--Gauss--Lobatto collocation methods for variable-order
fractional differential equations using a singular approximation basis in terms of weighted …