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 …

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of
the special functions with respect to another function, and the integro-differential operators …

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 …

Abstract Recently Caputo and Fabrizio introduced a new derivative with fractional order. In
this paper, we presented useful tools about the new derivative and applied it to the nonlinear …

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly
established fractional-order calculus operators involving singular and non-singular kernels …

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
provides a physical review of fractional operators, fractional variable order operators, and …

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 purpose of this note is to present the different fractional order derivatives definition that
are commonly used in the literature on one hand and to present a table of fractional order …