In this paper, we study a fractional order hybrid non-homogeneous ordinary diffe- rential equation. We gain r^ae^rt for the a order derivatives of both Riemann-Liouville type and Caputo type of function f（t） = e^rt ...In this paper, we study a fractional order hybrid non-homogeneous ordinary diffe- rential equation. We gain r^ae^rt for the a order derivatives of both Riemann-Liouville type and Caputo type of function f（t） = e^rt by letting integral lower limit of fractional derivative be -∞. It is first time for us to use the traditional eigenvalue method to solve fractional order ordinary differential equation. However, the law of the number of mutually independent arbitrary constants in general solutions to fractional order hy- brid non-homogeneous ordinary differential equation and general ordinary differential equation are very different.展开更多
基金jointly supported by the education department of Fujian provincial science and technology project Class A(JA13352)
文摘In this paper, we study a fractional order hybrid non-homogeneous ordinary diffe- rential equation. We gain r^ae^rt for the a order derivatives of both Riemann-Liouville type and Caputo type of function f（t） = e^rt by letting integral lower limit of fractional derivative be -∞. It is first time for us to use the traditional eigenvalue method to solve fractional order ordinary differential equation. However, the law of the number of mutually independent arbitrary constants in general solutions to fractional order hy- brid non-homogeneous ordinary differential equation and general ordinary differential equation are very different.
