Intelligent predictive computing for functional differential system in quantum calculus

被引：1
作者：
Asghar S.A. [1 ]
Ilyas H. [1 ]
Naz S. [1 ]
Raja M.A.Z. [2 ]
Ahmad I. [1 ]
Shaoib M. [3 ,4 ]
机构：
[1] Department of Mathematics, University of Gujrat, Gujrat
[2] Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Yunlin, Douliou
[3] Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock
[4] AI Center, Yuan Ze University, Taoyüan
来源：
Journal of Ambient Intelligence and Humanized Computing | 2024年 / 15卷 / 04期
关键词：
Levenberg–Marquardt backpropagation (LMB); Neural networks; Pantograph equations; Quantum calculus;
D O I：
10.1007/s12652-023-04744-0
中图分类号：
学科分类号：
摘要：
The aim of this study is to present a novel application of Levenberg–Marquardt backpropagation (LMB) to investigate numerically the solution of functional differential equations (FDE) arising in quantum calculus models (QCMs). The various types of discrete versions of FDM in QCMs are always found to be stiff to solve due to involvement of delay and to overcome the said difficulty, we proposed intelligent computing platform via LMB networks. In order to generate dataset for LMB networks, firstly, the FDEs in QCMs are converted into recurrence relations, then these recurrence systems are solved numerically on a specific input grids in case of both types of FDEs with q-exponential function as well as stable with decreasing behavior characteristics. The training, testing and validation samples based processes are employed to construct LMB networks by exploiting approximation theory on mean square error sense for obtaining the solutions of both types of FDEs. The exhaustive conducted simulation studies for solving FDEs in QCMs via absolute error and mean squared error endorse the accuracy, potential, convergence, stability and worth of proposed technique, which further certified through viable training state parameters, outcomes of error histograms, values of regression/correlation indices. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
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页码：2153 / 2168
页数：15
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共 89 条
  • [11] Ali S., Raja M.A.Z., Cheema T.N., Et al., Analysis of Williamson nanofluid with velocity and thermal slips past over a stretching sheet by Lobatto IIIA numerically, Therm Sci, 25, 4 Part A, pp. 2795-2805, (2021)
  • [12] Almutairi O.B., Quantum estimates for different type intequalities through generalized convexity, Entropy, 24, 5, (2022)
  • [13] Alp N., Budak H., Erden S., Et al., New bounds for q-midpoint-type inequalities via twice q-differentiable functions on quantum calculus, Soft Comput, 26, 19, pp. 10321-10329, (2022)
  • [14] Ansari H., Mokhtary P., Computational Legendre Tau method for Volterra Hammerstein pantograph integral equations, Bull Iran Math Soc, 45, pp. 475-493, (2019)
  • [15] Arbi A., Tahri N., New results on time scales of pseudo Weyl almost periodic solution of delayed QVSICNNs, Comput Appl Math, 41, 6, (2022)
  • [16] Asghar S.A., Naz S., Raja M.A.Z., Intelligent computing with the knack of Bayesian neural networks for functional differential systems in quantum calculus model, Int J Mod Phys B, 37, 22, (2023)
  • [17] Bahgat M.S., Approximate analytical solution of the linear and nonlinear multi-pantograph delay differential equations, Phys Scr, 95, 5, (2020)
  • [18] Bhatia M., Bhatia S., Hooda M., Et al., Analyzing and classifying MRI images using robust mathematical modeling, Multimed Tools Appl, 81, 26, pp. 37519-37540, (2022)
  • [19] Botmart T., Sabir Z., Raja M.A.Z., Et al., A numerical study of the fractional order dynamical nonlinear susceptible infected and quarantine differential model using the stochastic numerical approach, Fractal Fract, 6, 3, (2022)
  • [20] Bukhari A.H., Raja M.A.Z., Sulaiman M., Et al., Fractional neuro-sequential ARFIMA-LSTM for financial market forecasting, IEEE Access, 8, pp. 71326-71338, (2020)
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