研究了Riemman-Liouville型导数下的一类高次分数阶微分方程解的存在性问题,所涉及的阶数α为(3,4]的任意实数.给出了所给分数阶微分方程等价的Volterra积分形式,利用泛函分析中的经典方法建立了这类高次分数阶微分方程局部解的存在性定理.
This paper studies the existence of solutions of a class of higher order differential equations of fractional order derivative of the Riemman-Liouville type.The order numberα∈(3,4]is any real number.Firstly,we give the Voletrra integral form,which is the equivalent form of differential equations.Secondly,by using the classical method in functional analysis,we establish the existence theorem of local solutions of the higher-order fractional differential equations.