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Intelligent predictive computing for functional differential system in quantum calculus

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Abstract

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.

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  1. Syed Ali Asghar, Hira Ilyas, Shafaq Naz, Muhammad Asif Zahoor Raja, Iftikhar Ahmad and Muhammad Shaoib contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan

    Syed Ali Asghar, Hira Ilyas, Shafaq Naz & Iftikhar Ahmad

  2. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Muhammad Asif Zahoor Raja

  3. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Shaoib

  4. AI Center, Yuan Ze University, Taoyüan, 320, Taiwan, ROC

    Muhammad Shaoib

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  1. Syed Ali Asghar
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  2. Hira Ilyas
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Asghar, S.A., Ilyas, H., Naz, S. et al. Intelligent predictive computing for functional differential system in quantum calculus. J Ambient Intell Human Comput 15, 2153–2168 (2024). https://doi.org/10.1007/s12652-023-04744-0

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