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Numerical investigation of a fractional order differential human papillomavirus model using time delay neural network

Dostdar AliFaqir ShahDepartment of Mathematics, Karakoram International University, 15100 Gilgit, PakistanAsad UllahDepartment of Mathematics, Karakoram International University, 15100 Gilgit, PakistanShumaila JaveedDepartment of Mathematics, COMSATS University Islamabad, Islamabad Campus, Park Road, Chak Shahzad Islamabad, 45550, PakistanUme AyeshaDepartment of Mathematics, COMSATS University Islamabad, Islamabad Campus, Park Road, Chak Shahzad Islamabad, 45550, PakistanBarno Sayfutdinovna AbdullaevaDepartment of Mathematics and Information Technologies, Vice-Rector for Scientific Affairs, Tashkent State Pedagogical University, Tashkent, UzbekistanManish GuptaDivision of Research and Development, Lovely Professional University, Phagwara, IndiaNainaru TarakaramuDepartment of Mathematics, School of Liberal Arts and Science, Mohan Babu University, Sree Sainath Nagar, Tirupati, 517102, Andrapradesh, India

2025en

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Litsenziya: cc-by-nc-nd

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Annotatsiya

The objective of this study is to find the numerical results of a fractional order-dynamics model of the Human-papillomavirus (HPV) using time-delayed neural networks (TDNNs) in conjunction with the innovative Levenberg-Marquardt backpropagation (LMB) technique, referred to as TDNNs-LMB. The TDNNs-LMB procedure is carried out using training, validation, and testing data. The fractional-order dynamics model of HPV is analyzed for four distinct cases of fractional-order. In order to address the fractional-order HPV model, the dataset is partitioned into three segments with a split of 70 % allocated for training, 15 % set aside for validation, and another 15 % reserved for testing. A reference solution is established for the comparison of the results produced by the proposed neural network technique with the existing solutions of the HPV fractional model. The absolute error (AE) plots are provided to assess the accuracy and precision of the HPV fractional order-model. The obtained numerical solutions of the HPV model are evaluated in terms of mean square-error (MSE). The efficiency, reliability, and effectiveness of the TDNNs-LMB procedure are demonstrated through numerical performance metrics, including, fitting curves , correlation, state transitions (STs), error histograms (EHs), and MSE.

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DOI: 10.1016/j.padiff.2025.101196

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