deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations
This addresses the problem of accurately solving fractional differential equations for computational mathematics and engineering applications, representing an incremental advance.
The researchers tackled solving fractional differential equations by proposing a novel neural network architecture, achieving excellent precision across three equation forms.
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.