Artificial neural network for solving the nonlinear singular fractional differential equations

Althubiti, Saeed; Kumar, M Suresh; Goswami, Pranay; Kumar, Kranti

doi:10.1080/27690911.2023.2187389

Cited by 10 publications

(5 citation statements)

References 27 publications

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“…(2023) [38] demonstrated that to solve nonlinear singular fractional differential equations, increasing the number of hidden layers results in improved performance in terms of error. Similarly, Panghal and Kumar (2021) [39] observed improved accuracy when simulating a delay and first-order differential equation system with multiple hidden layers.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique

Kumar,

Goswami

2024

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, a deep artificial neural network technique is proposed to solve the coupled system of Emden-Fowler equations. A vectorized form of algorithm is developed. Implementation and simulation of this technique is performed using Python code. This technique is implemented in various numerical examples, and simulations are conducted. We have shown graphically how accurately this method works. We have shown the comparison of numerical solution and exact solution using error tables. We have also conducted a comparative analysis of our solution with alternative methods, including the Bernstein collocation method and the Homotopy analysis method. The comparative results are presented in error tables. The efficiency and accuracy of this method are demonstrated by these graphs and tables.

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Section: Numerical Illustrationsmentioning

confidence: 99%

Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique

Kumar,

Goswami

2024

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…the ANN-GAAS solver is accomplished to perform the highly nonlinear singular systems [ 46 , 47 ], biological differential models [ 48 , 49 ], nonlinear dynamics of the models [ [50] , [51] , [52] ], fractional differential model [ 53 , 54 ], cylindrical nonlinear Schrödinger equation [ 55 ], and pseudoplastic nanofluid flow [ 56 ].…”

Section: Future Research Directionmentioning

confidence: 99%

Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model

Sabir,

Baleanu,

E Alhazmi

et al. 2023

Heliyon

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“…One of the two primary types of artificial neural networks, a feedforward neural network, is distinguished by the way information is processed and sent between its various layers. Feedforward neural networks are structured as a sequence of interconnected layers (1)(2)(3)(4)(5)(6)(7). The initial layer is connected to the network's input, and each subsequent layer is linked to the one preceding it.…”

Section: Feed-forward Neural Networkmentioning

confidence: 99%

Artificial neural network with the Levenberg-Marquardtalgorithm for numerical solution of two-dimension Poisson’sequation

Thander

2023

BIJSCIT

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This study introduces an Artificial Neural Network (ANN) framework to address the two-dimensional Poisson’sequation within a rectangular domain. It places a focus on the training process of a neural network with threelayers, incorporating hidden neurons. The feedforward ANN is trained using MATLAB, which calculates weights forall neurons within the network structure. These acquired weights are subsequently applied in the trained networkmodel to make predictions for the desired output of a specific partial differential equation. The architecture of theANN consists of three layers: one input layer, one hidden layer, and one output layer. In this study, we specificallyemploy an ANN configuration with 50 hidden neurons. The training process is executed using MATLAB, utilizing theLevenberg–Marquardt algorithm (LMA) for optimization. Furthermore, the study encompasses the development ofsurface and contour plots that illustrate the computational solution of the partial differential equation. Additionally,error functions are graphed to assess the effectiveness of the ANN model.

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Artificial neural network for solving the nonlinear singular fractional differential equations

Cited by 10 publications

References 27 publications

Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique

Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique

Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model

Artificial neural network with the Levenberg-Marquardtalgorithm for numerical solution of two-dimension Poisson’sequation

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