Variable-order Fractional Operators Research Articles

Generalized fractional isoperimetric problem of several variables

This work deals with the generalized fractional calculus of variations of several variables. Precisely, we prove a sufficient optimality condition for the fundamental problem and a necessary optimality condition for the isoperimetric problem. Our results cover important particular cases of problems with constant and variable order fractional operators.

A Physical experimental study of variable-order fractional integrator and differentiator

Recent research results have shown that many complex physical phenomena can be better described using variable-order fractional differential equations. To understand the physical meaning of variable-order fractional calculus, and better know the application potentials of variable-order fractional operators in physical processes, an experimental study of temperature-dependent variable-order fractional integrator and differentiator is presented in this paper. The detailed introduction of analogue realization of variable-order fractional operator, and the influence of temperature to the order of fractional operator are presented in particular. Furthermore, the potential applications of variable-order fractional operators in PIλ(t)Dμ(t) controller and dynamic-order fractional systems are suggested.

Synthesis of multifractional Gaussian noises based on variable-order fractional operators

In this paper, a synthesis method, which is based on variable-order fractional operators, for multifractional Gaussian noises (mGn) is proposed by studying the relationship of white Gaussian noise (wGn), mGn, and multifractional Brownian motion (mBm). Furthermore, a synthesis method for multifractional α ‐ stable processes, the generalization of mGn, is proposed in order to more accurately characterize the processes with local scaling characteristics and heavy tailed distributions. Synthetic examples of mGn and multifractional α ‐ stable noises are provided for illustration.