关键词: 分数阶微分方程, 分离变量法, 常系数, 齐次线性

Abstract:

The authors investigated the solution structure of linear differential equations of fractional order in both time and spatial variables, and obtained some exact solutions via the approach of separating variables. For the exact solutions of invariable coefficient linear homogeneous fractional differential equations, the existence of general solutions and structural theorem of solutions were established by means of  undetermined special function method.

Key words: fractional differential equation, separate variable method, invariable coefficient, linear homogeneous