The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the proposed design. In each equation, a deep neural network is used to approximate the unknown function. Three forms of fractional differential equations have been examined to highlight the method's versatility: a fractional ordinary differential equation, a fractional order integrodifferential equation, and a fractional order partial differential equation. The results show that the proposed architecture solves different forms of fractional differential equations with excellent precision.

翻译：本研究的主要目标是提出一种能够精确求解分数阶微分方程的深度神经网络新型架构。在该架构设计中采用了高斯积分规则与$L_1$离散化技术。对于每个方程，使用深度神经网络逼近未知函数。为突出该方法的通用性，研究了三种形式的分数阶微分方程：分数阶常微分方程、分数阶积分微分方程与分数阶偏微分方程。结果表明，所提出架构能够以卓越的精度求解不同形式的分数阶微分方程。