一类具有双参数的有序分数阶微分方程初值问题

Initial Value Problems for a Class of Sequential Fractional Differential Equations with Two Parameters

研究了一类具有双参数的黎曼-刘维尔有序分数阶微分方程初值问题,利用分数阶积分算子,结合常微分方程的特征方程特征根方法和常数变易法,转换该问题为不动点问题,通过Schauder不动点定理,以及Banach压缩映射原理,得到了该初值问题解的存在性和唯一性充分条件,并举两例说明结果的应用。

The paper studies the initial value problem of a class of Riemann-Liouville sequential fractional differential equations with two parameters.Utilizing the fractional integral operator,combining the distinct real roots of the characteristic equation and variation of parameter technique,the above problem is transformed into an equivalent operator fixed point problem.By applying the Schauder fixed point theory and the Banach compression mapping principle,sufficient conditions of the existence and uniqueness for solution are obtained.Two examples are given to explain the application of the results.