On variational properties of balanced central fractional derivatives

ABSTRACTThis paper studies variational properties of naturally balanced fractional derivatives based on conventional left-sided and right-sided α-th order formulas, where α∈(12,1). 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.