A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models

The present work is to solve the nonlinear singular models using the framework of the stochastic computing approaches. The purpose of these investigations is not only focused to solve the singular models, but the solution of these models will be presented to the extended form of the delayed, predict...

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Main Authors: Zulqurnain Sabir, Hafiz Abdul Wahab, Juan L.G. Guirao
Format: Article
Language:English
Published: AIMS Press 2022-01-01
Series:Mathematical Biosciences and Engineering
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2022030?viewType=HTML
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author Zulqurnain Sabir
Hafiz Abdul Wahab
Juan L.G. Guirao
author_facet Zulqurnain Sabir
Hafiz Abdul Wahab
Juan L.G. Guirao
author_sort Zulqurnain Sabir
collection DOAJ
description The present work is to solve the nonlinear singular models using the framework of the stochastic computing approaches. The purpose of these investigations is not only focused to solve the singular models, but the solution of these models will be presented to the extended form of the delayed, prediction and pantograph differential models. The Gudermannian function is designed using the neural networks optimized through the global scheme "genetic algorithms (GA)", local method "sequential quadratic programming (SQP)" and the hybridization of GA-SQP. The comparison of the singular equations will be presented with the exact solutions along with the extended form of delayed, prediction and pantograph based on these singular models. Moreover, the neuron analysis will be provided to authenticate the efficiency and complexity of the designed approach. For the correctness and effectiveness of the proposed approach, the plots of absolute error will be drawn for the singular delayed, prediction and pantograph differential models. For the reliability and stability of the proposed method, the statistical performances "Theil inequality coefficient", "variance account for" and "mean absolute deviation'' are observed for multiple executions to solve singular delayed, prediction and pantograph differential models.
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spelling doaj.art-5e1dbf00669a434987c89ecb744754192022-12-22T04:10:11ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-01-0119166368710.3934/mbe.2022030A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential modelsZulqurnain Sabir0Hafiz Abdul Wahab 1Juan L.G. Guirao 21. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan1. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan2. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina 30203-Cartagena, Spain 3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaThe present work is to solve the nonlinear singular models using the framework of the stochastic computing approaches. The purpose of these investigations is not only focused to solve the singular models, but the solution of these models will be presented to the extended form of the delayed, prediction and pantograph differential models. The Gudermannian function is designed using the neural networks optimized through the global scheme "genetic algorithms (GA)", local method "sequential quadratic programming (SQP)" and the hybridization of GA-SQP. The comparison of the singular equations will be presented with the exact solutions along with the extended form of delayed, prediction and pantograph based on these singular models. Moreover, the neuron analysis will be provided to authenticate the efficiency and complexity of the designed approach. For the correctness and effectiveness of the proposed approach, the plots of absolute error will be drawn for the singular delayed, prediction and pantograph differential models. For the reliability and stability of the proposed method, the statistical performances "Theil inequality coefficient", "variance account for" and "mean absolute deviation'' are observed for multiple executions to solve singular delayed, prediction and pantograph differential models.https://www.aimspress.com/article/doi/10.3934/mbe.2022030?viewType=HTMLgudermannian neural networkssingular modelsglobal schemelocal approachneuron analysiscomplexity analysisstatistical performances
spellingShingle Zulqurnain Sabir
Hafiz Abdul Wahab
Juan L.G. Guirao
A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
Mathematical Biosciences and Engineering
gudermannian neural networks
singular models
global scheme
local approach
neuron analysis
complexity analysis
statistical performances
title A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
title_full A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
title_fullStr A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
title_full_unstemmed A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
title_short A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
title_sort novel design of gudermannian function as a neural network for the singular nonlinear delayed prediction and pantograph differential models
topic gudermannian neural networks
singular models
global scheme
local approach
neuron analysis
complexity analysis
statistical performances
url https://www.aimspress.com/article/doi/10.3934/mbe.2022030?viewType=HTML
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