Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

2021 ◽  
Author(s):  
C. J. Zúñiga-Aguilar ◽  
J. F. Gómez-Aguilar ◽  
H. M. Romero-Ugalde ◽  
R. F. Escobar-Jiménez ◽  
G. Fernández-Anaya ◽  
...  
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Differential Equations ◽  
Numerical Solution ◽  
Variable Order ◽  
Artificial Neural

Solving fractional differential equations of variable-order involving operators with Mittag-Leffler kernel using artificial neural networks

2017 ◽  
Vol 103 ◽  
pp. 382-403 ◽  
Author(s):  
C.J. Zúñiga-Aguilar ◽  
H.M. Romero-Ugalde ◽  
J.F. Gómez-Aguilar ◽  
R.F. Escobar-Jiménez ◽  
M. Valtierra-Rodríguez
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Variable Order ◽  
Fractional Differential ◽  
Artificial Neural

scholarly journals Application of ANNs approach for wave-like and heat-like equations

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 1086-1094 ◽  
Author(s):  
Ahmad Jafarian ◽  
Dumitru Baleanu
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Partial Differential ◽  
Artificial Neural ◽  
Initial Boundary Value

Abstract Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Numerical solution of hypersonic flows via artificial neural networks

2020 ◽  
Author(s):  
Ersin Ozbenli ◽  
Prakash Vedula ◽  
Konstantinos Vogiatzis ◽  
Eswar Josyula
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Numerical Solution ◽  
Hypersonic Flows ◽  
Artificial Neural
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