Analysis of fractional differential equations with multi-orders
Analysis of fractional differential equations with multi-orders
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DOI：
10.1142/s0218348x07003472
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发表时间：
2007-06-01
影响因子：
4.7
通讯作者：
Guo, Qian
中科院分区：
文献类型：
--
作者：
Deng, Weihua;Li, Changpin;Guo, Qian
本文研究了两类多阶分数阶微分系统。一个是多阶分数阶微分方程组，D-*((α)over bar)(X)over bar(T)=(F)over bar(t，(X)over bar(T)，(X)over bar(0)=(X)over bar(0)；另一个是多阶分数阶微分方程组，D(*)(beta*)y(T)=g(t，y(T))，D(*)(Beta 1)y(T)，…，D-*(Beta N)y(T))。利用这种技巧，只要多阶为有理数，这两类分数阶微分方程组就可以化为相同分数阶的方程，从而使已知的存在唯一性和对初始条件的依赖性定理易于应用。和它们的相伴线性系统的渐近稳定性定理，环BAR(T)上的D-*((α)环)(X)=环BAR(T)上的A(X)，环BAR(0)上的(X)=(X)环BAR(0)上的(X)，以及D-*(beta*)y(T)+Sigma(N)(i=1)a(I)D(*)(Beta I)y(T)，y(K)(0)=y(0)((K))，k=0，1，…，[beta*]-1，也得到了相应的结果。
In this paper, we study two kinds of fractional differential systems with multi- orders. One is a system of fractional differential equations with multi- order, D-*((alpha) over bar)(x) over bar (t)=(f) over bar (t,(x) over bar), (x) over bar (0)=(x) over bar (0); the other is a multi-order fractional differential equation, D(*)(beta*)y(t)=g(t,y(t)), D(*)(beta 1)y(t),...,D-*(beta n) y(t)). By the derived technique, such two kinds of fractional differential equations can be changed into equations with the same fractional orders providing that the multi-orders are rational numbers, so the known theorems of existence, uniqueness and dependence upon initial conditions are easily applied. And asymptotic stability theorems for their associate linear systems, D-*((alpha) over bar)(x) over bar (t)=A (x) over bar (t), (x) over bar (0)=(x) over bar (0), and D-*(beta*) y(t)=a(0)y(t)+Sigma(n)(i=1) a(i)D(*)(beta i)y(t), y((k))(0)=y(0)((k)), k=0, 1, ..., [beta*]-1, are also derived.