【摘要】 近年来，随着分数阶非线性微分方程的快速发展及其在众多科学领域中的广泛应用，分数阶非线性微分方程得到了越来越多学者的关注.该文通过不动点定理证明了一类含双Caputo分数阶导数的非线性微分方程初值问题解的存在唯一性、Ulam-Hyers稳定性；应用L1插值方法逼近Caputo分数阶导数，构造了求解含双Caputo分数阶导数的非线性微分方程的L1差分算法，并证明了方法的稳定性和收敛性.更多还原

【Abstract】 In recent years, with the rapid development of fractional nonlinear differential equations and their wide application in many scientific fields, fractional-order nonlinear differential equations have attracted more and more scholars’ attention. In this paper, we prove the existence and uniqueness, Ulam-Hyers stability of a class of nonlinear differential equation with two Caputo fractional derivatives by means of the fixed-point theorem. The L1 difference method for the nonlinear differential equation with two Caputo fractional derivatives is constructed by applying the L1 interpolation to approximate the Caputo fractional derivatives. The stability and convergence of the numerical method are proved.更多还原