Browsing by Author "Sabir, Zulqurnain"

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A hybrid computing approach to design the novel second order singular perturbed delay differential Lane-Emden model
(2022) Baleanu, Dumitru; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Hincal, Evren; 56389
In this study, the mathematical form of the second order perturbed singular delay differential system is presented. The comprehensive features using the singular-point, perturbed factor and pantograph term are provided together with the shape factor of the second order perturbed singular delay differential system. The novel model is simulated numerically through the artificial neural networks (ANNs) based on the global/local optimization procedures, i.e., genetic algorithm (GA) and sequential quadratic programming (SQP). An activation function is constructed by using the differential model based on the second order perturbed singular delay differential system. The optimization of fitness function is performed through the hybrid computing strength of the ANNs-GA-SQP to solve the second order perturbed singular delay differential system. The exactness, substantiation, and authentication of the novel system is observed to solve three different variants of the novel model. The convergence, robustness, correctness, and stability of the numerical approach is performed using the comparison procedures of the available exact solutions. For the reliability, the statistical performances with necessary processes are provided using the ANNs-GA-SQP.
A New Stochastic Computing Paradigm for the Dynamics of Nonlinear Singular Heat Conduction Model of the Human Head
(Springer Heidelberg, 2018) Baleanu, Dumitru; Umar, Muhammad; Sabir, Zulqurnain; Khan, Junaid Ali; Baleanu, Dumitru; 56389
Bio-inspired computing approaches are effective to solve a variety of dynamical problems. The strength of these stochastic solvers is exploited for the numerical treatment of a nonlinear heat conduction model of the human head using artificial neural networks (ANNs), genetic algorithms (GAs), active-set technique (AST), and their hybrids. The universal function approximation competencies of unsupervised ANNs are utilized in constructing the mathematical model of the problem by defining an error function in the mean squared sense. The training of the design parameters of ANN models is made with global search brilliance of GAs, viably local search with AST and hybrid approach GA-AST. The results of the proposed schemes are determined in terms of temperature profiles by considering variants of the problem with different Biot numbers, metabolic thermogenesis slope parameters and thermogenesis heat production factors. The correctness, effectiveness and convergence of the proposed approaches are also ascertained through statistics.
A novel computing stochastic algorithm to solve the nonlinear singular periodic boundary value problems
(2022) Baleanu, Dumitru; Baleanu, Dumitru; Ali, Mohamed R.; Sadat, R.; 56389
In this work, a class of singular periodic nonlinear differential systems (SP-NDS) in nuclear physics is numerically treated by using a novel computing approach based on the Gudermannian neural networks (GNNs) optimized by the mutual strength of global and local search abilities of genetic algorithms (GA) and sequential quadratic programming (SQP), i.e. GNNs-GA-SQP. The stimulation of offering this numerical computing work comes from the aim of introducing a consistent framework that has an effective structure of GNNs optimized with the backgrounds of soft computing to tackle such thought-provoking systems. Two different problems based on the SPNDS in nuclear physics will be examined to check the proficiency, robustness and constancy of the GNNs-GA-SQP. The outcomes obtained through GNNs-GA-SQP are compared with the true results to find the worth of designed procedures based on the multiple trials.
A novel radial basis procedure for the SIRC epidemic delay differential model
(2023) Baleanu, Dumitru; Baleanu, Dumitru; Mallawi, Fouad Othman; Ullah, Malik Zaka; 56389
The purpose of this work is to construct a reliable stochastic framework for solving the SIRC delay differential epidemic system, i.e. SIRC-DDES that is based on the coronavirus dynamics. The design of radial basis (RB) transfer function with the optimization of Bayesian regularization neural network (RB-BRNN) is presented to solve the SIRC-DDES. The SIRC-DDES is classified into susceptible $ S(x) $ S(x), infected $ I(x) $ I(x), recovered $ R(x) $ R(x) and cross-immune $ C(x) $ C(x). The exactness of the RB-BRNN is performed for three cases of SIRC-DDES by using the performances of the obtained and reference results. The mean square error is reduced by using the training, testing and substantiation performances with the reference solutions. The small values of the absolute error around 10-07 to 10-08 and different statistical operator performances based on the error histogram values, transitions of state investigations, correlation and regression tests also approve the accuracy of the proposed technique.
Applications Of Gudermannian Neural Network For Solving The Sitr Fractal System
(2021) Baleanu, Dumitru; Umar, Muhammad; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; 56389
This study is related to explore the Gudermannian neural network (GNN) for solving a nonlinear SITR COVID-19 fractal system by using the optimization efficiencies of a genetic algorithm (GA), a global search technique and sequential quadratic programming (SQP) and a quick local search scheme, i.e. GNN-GA-SQP. The nonlinear SITR COVID-19 fractal system is dependent on four collections: "susceptible", "infected", "treatment"and "recovered". For the optimization procedures through the GNN-GA-SQP, a merit function is constructed using the nonlinear SITR COVID-19 fractal system and its corresponding initial conditions. The description of each collection of the nonlinear SITR COVID-19 fractal system is provided along with comprehensive detail. The comparison of the achieved numerical result performances of each collection of the nonlinear SITR COVID-19 fractal system is performed with the Adams results to verify the exactness of the designed computational GNN-GA-SQP. The statistical processes based on different operators are presented for 30 independent trials using 5 neurons to authenticate the consistency of the designed computational GNN-GA-SQP. Moreover, the graphs of absolute error (AE), performance indices, and convergence measures along with the boxplots and histograms are also plotted to check the stability, exactness and reliability of the designed computational GNN-GA-SQP.
Computational Performances Of Morlet Wavelet Neural Network For Solving A Nonlinear Dynamic Based On The Mathematical Model Of The Affection Of Layla And Majnun
(2023) Baleanu, Dumitru; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Alshomrani, Ali S.; Hincal, Evren; 56389
The aim of this study is to design a novel stochastic solver through the Morlet wavelet neural networks (MWNNs) for solving the mathematical Layla and Majnun (LM) system. The numerical representations of the mathematical LM system have been presented by using the MWNNs along with the optimization is performed through the hybridization of the global and local search schemes. The local active-set (AS) and global genetic algorithm (GA) operators have been used to optimize an error-based merit function using the differential LM model and its initial conditions. The correctness of the MWNNs using the local and global operators is observed through the comparison of the obtained solutions and the Adams scheme, which is used as a reference solution. For the stability of the MWNNs using the global and local operators, the statistical performances with different operators have been provided using the multiple executions to solve the nonlinear LM system.
Design of Gudermannian Neuroswarming to solve the singular Emden-Fowler nonlinear model numerically
(2021) Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Cengiz, Korhan; Shoaib, Muhammad; 56389
The current investigation is related to the design of novel integrated neuroswarming heuristic paradigm using Gudermannian artificial neural networks (GANNs) optimized with particle swarm optimization (PSO) aid with active-set (AS) algorithm, i.e., GANN-PSOAS, for solving the nonlinear third-order Emden-Fowler model (NTO-EFM) involving single as well as multiple singularities. The Gudermannian activation function is exploited to construct the GANNs-based differential mapping for NTO-EFMs, and these networks are arbitrary integrated to formulate the fitness function of the system. An objective function is optimized using hybrid heuristics of PSO with AS, i.e., PSOAS, for finding the weights of GANN. The correctness, effectiveness and robustness of the designed GANN-PSOAS are verified through comparison with the exact solutions on three problems of NTO-EFMs. The assessments on statistical observations demonstrate the performance on different measures for the accuracy, consistency and stability of the proposed GANN-PSOAS solver.
Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model
(2022) Baleanu, Dumitru; Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; 56389
This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley–Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.
DESIGN OF NEURO-SWARMING HEURISTIC SOLVER FOR MULTI-PANTOGRAPH SINGULAR DELAY DIFFERENTIAL EQUATION
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Guirao, Juan L. G.; 56389
This research work is to design a neural-swarming heuristic procedure for numerical investigations of Singular Multi-Pantograph Delay Differential (SMP-DD) equation by applying the function approximation aptitude of Artificial Neural Networks (ANNs) optimized efficient swarming mechanism based on Particle Swarm Optimization (PSO) integrated with convex optimization with Active Set (AS) algorithm for rapid refinements, named as ANN-PSO-AS. A merit function (MF) on mean squared error sense is designed by using the differential ANN models and boundary condition. The optimization of this MF is executed with the global PSO and local search AS approaches. The planned ANN-PSO-AS approach is instigated for three different SMP-DD model-based equations. The assessment with available standard results relieved the effectiveness, robustness and precision that is further authenticated through statistical investigations of Variance Account For, Root Mean Squared Error, Semi-Interquartile Range and Theil's inequality coefficient performances.
Design of stochastic numerical solver for the solution of singular three-point second-order boundary value problems
(2020) Baleanu, Dumitru; Baleanu, Dumitru; Shoaib, Muhammad; Raja, Muhammad Asif Zahoo; 56389
In this paper, a novel meta-heuristic computing solver is presented for solving the singular three-point second-order boundary value problems using artificial neural networks (ANNs) optimized by the combined strength of global and local search ability of genetic algorithms (GAs) and interior point algorithm (IPA), i.e., ANN-GA-IPA. The inspiration for presenting this numerical work comes from the intention of introducing a consistent framework that combines the effective features of neural networks optimized with the contexts of soft computing to handle with such challenging systems. Three numerical variants of singular second-order system have been taken to examine the proficiency, robustness, and stability of the designed approach. The comparison of the proposed results of ANN-GA-IPA from available exact solutions shows the good agreement with 5 to 7 decimal places of the accuracy which established worth of the methodology through performance analyses on a single and multiple executions.
Dynamics of multi-point singular fifth-order Lane–Emden system with neuro-evolution heuristics
(2022) Baleanu, Dumitru; Ali, Mohamed R.; Fathurrochman, Irwan; Raja, Muhammad Asif Zahoor; Sadat, R.; Baleanu, Dumitru; 56389
The objective of the presented communication is to examine and analyze the solutions of nonlinear multi-singular fifth-order Lane–Emden (LE) system for different scenarios by variation of shape factors settled on the equivalent design of the LE equations. The neuro-evolution based stochastic computing is explored for the numerical measures using the artificial neural networks (ANNs) models for the appropriate continuous mapping, while the learning of decision variables is conducted using the integrated meta-heuristic global search of genetic algorithms (GA) hybrid with the local search efficiency of active-set (AS) i.e., ANN-GA-AS scheme. The numerical approach ANN-GA-AS is applied efficiently for the fifth kind of nonlinear LE model and statistical calculations further validate the accuracy, robustness as well as convergence.
Dynamics of three-point boundary value problems with Gudermannian neural networks
(2023) Baleanu, Dumitru; Ali, Mohamed R.; Raja, Muhammad Asif Zahoor; Sadat, R.; Baleanu, Dumitru; 56389
The present study articulates a novel heuristic computing design with artificial intelligence algorithm by manipulating the models with Feed forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of Genetic algorithms (GA) combined with rapid local convergence of Active-set method (ASM), i.e., FF-GNN-GAASM for solving the second kind of Three-point singular boundary value problems (TPS-BVPs). The proposed FF-GNN-GAASM intelligent computing solver integrated into the hidden layer structure of FF-GNN systems of differential operatives of the second kind of STP-BVPs, which are linked to form the error based Merit function (MF). The MF is optimized with the hybrid-combined heuristics of GAASM. The stimulation for presenting this research work comes from the objective to introduce a reliable framework that associates the operational features of NNs to challenge with such inspiring models. Three different measures of the second kind of TPS-BVPs is applied to assess the robustness, correctness and usefulness of the designed FF-GNN-GAASM. Statistical evaluations through the performance of FF-GNN-GAASM is validated via consistent stability, accuracy and convergence.
Evolutionary computing for nonlinear singular boundary value problems using neural network, genetic algorithm and active-set algorithm
(2021) Baleanu, Dumitru; Khalique, Chaudry Masood; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; 56389
In this numerical study, a class of nonlinear singular boundary value problem is solved by implementation of a novel meta-heuristic computing tool based on the artificial neural networks (ANNs) modeling of system and the optimization of decision variable of ANNs through the combined strength of global search via genetic algorithms (GA) and local search ability of active-set algorithm (ASA), i.e., ANN–GA–ASA. The proposed intelligent computing solver ANN–GA–ASA exploits the input, hidden, and output layers’ structure of ANNs. This is to represent the differential model in the nonlinear singular second-order periodic boundary value problems, which are connected to form an error-based objective function (OF) and optimize the OF by the integrated heuristics of GA–ASA. The purpose to present this research is to associate the operational legacy of neural networks and to challenge such kinds of inspiring models. Two different examples of the singular periodic model have been investigated to observe the robustness, proficiency and stability of the ANN–GA–ASA. The proposed outcomes of ANN–GA–ASA are compared with reference to true results so as to establish the value of the designed scheme. Exhaustive comparison has been made and presented between the Log-sigmoidal ANNs results and the radial basis ANNs outcomes. The reliability of the results obtained is endorsed by using both types of networks as well as the value of designed schemes. © 2021, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
FMNSICS: Fractional Meyer neuro-swarm intelligent computing solver for nonlinear fractional Lane–Emden systems
(2022) Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Umar, Muhammad; Shoaib, Muhammad; Baleanu, Dumitru; 56389
The fractional neuro-evolution-based intelligent computing has substantial potential to solve fractional order systems represented with Lane–Emden equation arising in astrophysics including Newtonian self-gravitating, spherically symmetric and polytropic fluid. The present study aimed to present a neuro-swarm-based intelligent computing solver for the solution of nonlinear fractional Lane–Emden system (NFLES) using by exploitation of fractional Meyer wavelet artificial neural networks (FMW-ANNs) and global optimization mechanism of particle swarm optimization (PSO) combined with rapid local search of sequential quadratic programming (SQP), i.e., FMW-ANN-PSO-SQP. The motivation for the design of FMW-ANN-PSO-SQP intelligent computing comes with an objective of presenting an accurate, reliable, and viable framworks to deal with stiff nonlinear singular models represented with NFLES involving both fractional and integer derivative terms. The designed algorithm is tested for six different variants of NFLESs. The obtained numerical outcomes obtained by the proposed FMW-ANN-PSO-SQP are compared with the exact results to authenticate the correctness, efficacy, and viability, and these aspects are further endorsed statistical observations. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
Fractional Mayer Neuro-Swarm Heuristic Solver for Multi-Fractional Order Doubly Singular Model Based on Lane-Emden Equation_net
(2021) Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; 56389
This research is related to present a novel fractional Mayer neuro-swarming intelligent solver for the numerical treatment of multi-fractional order doubly singular Lane-Emden (LE) equation using combined investigations of the Mayer wavelet (MW) neural networks (NNs) optimized by the global search effectiveness of particle swarm optimization (PSO) and interior-point (IP) method, i.e. MW-NN-PSOIP. The design of novel fractional Mayer neuro-swarming intelligent solver for multi-fractional order doubly singular LE equation is derived from the standard LE model and the shape factors; fractional order terms along with singular points are examined. The modeling based on the MW-NN strength is implemented to signify the multi-fractional order doubly singular LE model using the ability of mean squared error in terms of the merit function and the networks are optimized with the integrated capability of PSOIP scheme. The perfection, verification and validation of the fractional Mayer neuro-swarming intelligent solver for three different cases of the multi-fractional order doubly singular LE equation are recognized through comparative investigations from the reference results on different measures based on the convergence, robustness, stability and accuracy. Furthermore, the statics interpretations further validate the performance of the proposed fractional Mayer neuro-swarming intelligent solvers. © 2021 The Author(s).
Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model
(2023) Baleanu, Dumitru; Baleanu, Dumitru; E Alhazmi, Sharifah; Ben Said, Salem; 56389
The current study shows a reliable stochastic computing heuristic approach for solving the nonlinear Rabinovich-Fabrikant model. This nonlinear model contains three ordinary differential equations. The process of stochastic computing artificial neural networks (ANNs) has been applied along with the competences of global heuristic genetic algorithm (GA) and local search active set (AS) methodologies, i.e., ANNs-GAAS. The construction of merit function is performed through the differential Rabinovich-Fabrikant model. The results obtained through this scheme are simple, reliable, and accurate, which have been calculated to optimize the merit function by using the GAAS method. The comparison of the obtained results through this scheme and the conventional reference solutions strengthens the correctness of the proposed method. Ten numbers of neurons along with the log-sigmoid transfer function in the neural network structure have been used to solve the model. The values of the absolute error are performed around 10−07 and 10−08 for each class of the Rabinovich-Fabrikant model. Moreover, the reliability of the ANNs-GAAS approach is observed by using different statistical approaches for solving the Rabinovich-Fabrikant model.
Investigations Of Non-Linear Induction Motor Model Using The Gudermannıan Neural Networks
(2022) Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Sadat, Rahma; Ali, Mohamed R.; 56389
This study aims to solve the non-linear fifth-order induction motor model (FO-IMM) using the Gudermannian neural networks (GNN) along with the optimization procedures of global search as a genetic algorithm together with the quick local search process as active-set technique (GNN-GA-AST). The GNN are executed to discretize the non-linear FO-IMM to prompt the fitness function in the procedure of mean square error. The exactness of the GNN-GA-AST is observed by comparing the obtained results with the reference results. The numerical performances of the stochastic GNN-GA-AST are provided to tackle three different variants based on the non-linear FO-IMM to authenticate the consistency, significance and efficacy of the designed stochastic GNN-GA-AST. Additionally, statistical illustrations are available to authenticate the precision, accuracy and convergence of the designed stochastic GNN-GA-AST.
Meyer Wavelet Neural Networks Procedures To Investigate The Numerical Performances Of The Computer Virus Spread With Kill Signals
(2023) Baleanu, Dumitru; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Alshomrani, Ali S.; Hincal, Evren; 56389
This study shows the design of the Meyer wavelet neural networks (WNNs) to perform the numerical solutions of the spread of computer virus with kill signals, i.e. SEIR-KS system. The optimization of the SEIR-KS system is performed by the Meyer WNNs together with the optimization through the genetic algorithm (GA) and sequential quadratic (SQ) programming, i.e. Meyer WNNs-GASQ programming. A sigmoidal-based log-sigmoid function is implemented as an activation function, while 10 numbers of neurons work with 120 variables throughout this study. The correctness of the proposed Meyer WNNs-GASQP programming is observed through the comparison of the obtained and reference numerical solutions. For the consistency and reliability of the Meyer WNNs-GASQ programming, an analysis based on different statistical procedures is performed using 40 numbers of independent executions. Moreover, the use of different statistical operators like mean, median, minimum, standard deviation and semi-interquartile range further validates the correctness of the Meyer WNNs-GASQ programming for solving the SEIR-KS system.
Numerical Computational Heuristic Through Morlet Wavelet Neural Network for Solving the Dynamics of Nonlinear SITR COVID-19
(2022) Baleanu, Dumitru; Alnahdi, Abeer S.; Jeelani, Mdi Begum; Abdelkawy, Mohamed A.; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Hussain, Muhammad Mubashar; 56389
The present investigations are associated with designing Morlet wavelet neural network (MWNN) for solving a class of susceptible, infected, treatment and recovered (SITR) fractal systems of COVID-19 propagation and control. The structure of an error function is accessible using the SITR differential form and its initial conditions. The optimization is performed using the MWNN together with the global as well as local search heuristics of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. The detail of each class of the SITR nonlinear COVID-19 system is also discussed. The obtained outcomes of the SITR system are compared with the Runge-Kutta results to check the perfection of the designed method. The statistical analysis is performed using different measures for 30 independent runs as well as 15 variables to authenticate the consistency of the proposed method. The plots of the absolute error, convergence analysis, histogram, performance measures, and boxp
Numerical solutions of a novel designed prevention class in the HIV nonlinear model
(2021) Baleanu, Dumitru; Umar, Muhammad; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; 56389
The presented research aims to design a new prevention class (P) in the HIV nonlinear system, i.e., the HIPV model. Then numerical treatment of the newly formulated HIPV model is portrayed handled by using the strength of stochastic procedure based numerical computing schemes exploiting the artificial neural networks (ANNs) modeling legacy together with the optimization competence of the hybrid of global and local search schemes via genetic algorithms (GAs) and active-set approach (ASA), i.e., GA-ASA. The optimization performances through GA-ASA are accessed by presenting an error-based fitness function designed for all the classes of the HIPV model and its corresponding initial conditions represented with nonlinear systems of ODEs. To check the exactness of the proposed stochastic scheme, the comparison of the obtained results and Adams numerical results is performed. For the convergence measures, the learning curves are presented based on the different contact rate values. Moreover, the statistical performances through different operators indicate the stability and reliability of the proposed stochastic scheme to solve the novel designed HIPV model. © 2021 Tech Science Press. All rights reserved.