A Hybrid Fractional Differentiation
The fractional differentiations include integration. We propose a differentiation, in which the interval of integration is divided into subintervals and different type of fractional derivative is de.ned in each subinterval. An example is given by hDqaf(t)=d/dt c∫a (t-τ)-q/Γ(1-q)f(τ)dτ+t∫c (t-τ)-q/Γ(1-q)f(1)(τ)dτ(1)for 0 < q < 1 and c ∈ (a, t). This type of de.nition is convenient for numerical calculation of fractional differentiation. The second term ensures accurate estimation at t with use of current data points. The time differentiation in the .rst term can be replaced by the derivative of integrand. Thus, the derivative can also be calculated by the current data. The kernel is given by (t-τ )-1-q, which enable smaller contribution of old f(τ ) compared with that of the Caputo derivative. It can be shown that (1) is related to the Riemann-Liouville derivative in a certain condition.
Fractional differentiation fractional integration Riemann-Liouville derivative Caputo derivative numerical simulation integration algorithm.
Masataka Fukunaga Nobuyuki Shimizu
College of Engineering, Nihon University(P.T. Lecturer),(home)1-2-35-405, Katahira, Aoba-ku, Sendai, Department of Mechanical Systems and Design Engineering, Iwaki Meisei University, Iwaki, 970-8551, J
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-4
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）