【摘要】 本文基于现有的切比雪夫神经网络,提出了一种利用遗传算法优化切比雪夫神经网络求解分数阶Bagley-Torvik方程数值解的新方法,结合多点处的泰勒公式原理,给出数值解的一般形式,将原问题转化为求解无约束最小化问题.与现有数值方法的数值结果进行比较表明了本文方法的可行性和有效性,为分数阶微分方程中类似问题的求解提供了新的思路.更多还原

【Abstract】 In this article,based on the existing Chebyshev neural network,a new method using genetic algorithm to optimize the Chebyshev neural network to solve the numerical solution of fractional Bagley-Torvik equation is proposed.Combined with the Taylor ’s formula principle at multiple points,the general form of numerical solution is given,and the original problem is transformed into an unconstrained minimization problem.The comparison with the numerical results of the existing numerical methods shows the feasibility and effectiveness of the proposed method,which provides a new idea for the solution of similar problems in fractional differential equations.更多还原