Analysis of fractional differential equations with multi-orders. (English) Zbl 1176.34008
Summary: We study two kinds of fractional differential systems with multi-orders. One is a system of fractional differential equations with multi-order, ; the other is a multi-order fractional differential equation, . 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, , and , are also derived.
|34A25||Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)|
|34M99||Differential equations in the complex domain|