ABSTRACT
This paper studies variational properties of naturally balanced fractional derivatives based on conventional left-sided and right-sided α-th order formulas, where Approximations of fractional differential equations equipped with such naturally balanced fractional derivatives are investigated via Ritz–Galerkin approaches. It is found that not only the balanced fractional derivatives possess important variational properties, equations equipped with them exhibit desirable dynamic features as a Ritz–Galerkin formula being applied. Simulation experiments are given to illustrate our conclusions and results.
Acknowledgments
The authors would like also to thank Prof. Guanghui Hu, University of Macau, for his suggestions in the preparation of this manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. An alternative estimation of is given by
Therefore, we have