deepFDEnet: A Novel Neural Network Architecture for Solving Fractional
  Differential Equations
Ali Nosrati Firoozsalari Hassan Dana Mazraeh Alireza Afzal Aghaei Kourosh Parand
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.