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.
• NeuralNetwork Method • Numerical Solutions • Fractional Differential Equations
• NeuralNetwork Method • Numerical Solutions • Fractional Differential Equations
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik / Mathematics |
Yazarlar | |
Erken Görünüm Tarihi | 27 Mayıs 2023 |
Yayımlanma Tarihi | 1 Haziran 2023 |
Gönderilme Tarihi | 6 Ocak 2023 |
Kabul Tarihi | 23 Şubat 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 13 Sayı: 2 |