Investigation of Solutions of 𝜷 −conformable Fractional Ordinary Differential Equation With Artificial Neural Network

Year 2023, Volume: 13 Issue: 2, 1266 - 1274, 01.06.2023

Sadullah Bulut , Muhammed Yiğider

https://doi.org/10.21597/jist.1230287

Abstract

İn this study, we present a method in order to get initial value fractional differential equations with artificial neural networks. On the basis of the function approach of feedforward neural networks, this method is a general method that is written in an implicit analytical form and results in the creation of a differentiable solution. The first part of the created trial solution which is stated as the sum of the two parts, with no controllable parameters, gives the initial conditions. The second part, unaffected by the initial conditions, consists of a feedforward neural network with controllable parameters (weights). The applicability of this approach is demonstrated in systems of both fractional single ODEs and fractional coupled ODEs.

Keywords

• NeuralNetwork Method, • Numerical Solutions, • Fractional Differential Equations

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