Journal ArticleDOI
Solving fractional differential equations of variable-order involving operators with Mittag-Leffler kernel using artificial neural networks
C. J. Zúñiga-Aguilar,H. M. Romero-Ugalde,José Francisco Gómez-Aguilar,Ricardo Fabricio Escobar-Jiménez,Martin Valtierra-Rodriguez +4 more
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TLDR
In this article, a new neural network approach was proposed to approximate the solution of fractional differential equations using a new approach of artificial neural network and the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method.Abstract:
In this paper, we approximate the solution of fractional differential equations using a new approach of artificial neural network. We consider fractional differential equations of variable-order with Mittag-Leffler kernel in Liouville–Caputo sense. With this new neural network approach, it is obtained an approximate solution of the fractional differential equation and this solution is optimized using the Levenberg–Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional differential equations, the Willamowski-Rossler oscillator and a multi-scroll system. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network different performance indices were calculated.read more
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Journal ArticleDOI
Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization.
TL;DR: A new three-dimensional fractional-order Hopfield-type neural network with delay is proposed, which has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable.
Journal ArticleDOI
A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics
Muhammad Umar,Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Shoaib,Manoj Gupta,Yolanda Guerrero Sánchez +5 more
TL;DR: The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials.
Journal ArticleDOI
FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system
Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,Muhammad Shoaib,J. F. Gómez Aguilar +4 more
TL;DR: The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures, and the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.
Journal ArticleDOI
Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system
Ayaz Hussain Bukhari,Muhammad Sulaiman,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,Saeed Islam,Muhammad Shoaib,Poom Kumam,Poom Kumam +7 more
TL;DR: An integrated bi-modal computing paradigm based on Nonlinear Autoregressive Radial Basis Functions (NAR-RBFs) neural network model, a new family of deep learning with the strength of hybrid artificial neural network is presented for the solution of nonlinear chaotic dusty system (NCDS) of tiny ionized gas particles arising in fusion devices, industry, astronomy and space.
Journal ArticleDOI
A novel design of fractional Meyer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems
Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,Juan Luis García Guirao,Muhammad Shoaib +4 more
TL;DR: A novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network is designed for nonlinear-singular fractional Lane-Emden (NS-FLE) differential equation to validate the worth of FMW-ANN-GASA for the solution of singular nonlinear fractional order systems.
References
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Proceedings Article
ImageNet Classification with Deep Convolutional Neural Networks
TL;DR: The state-of-the-art performance of CNNs was achieved by Deep Convolutional Neural Networks (DCNNs) as discussed by the authors, which consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax.
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Multi-column deep neural networks for image classification
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Journal ArticleDOI
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana,Dumitru Baleanu +1 more
TL;DR: In this article, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.
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