{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:08:52Z","timestamp":1773929332054,"version":"3.50.1"},"reference-count":37,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T00:00:00Z","timestamp":1771372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz University","doi-asserted-by":"publisher","award":["(PSAU\/2025\/01\/38405)"],"award-info":[{"award-number":["(PSAU\/2025\/01\/38405)"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Neuroinform."],"abstract":"<jats:p>\n                    This study presents a novel fractional order model of Alzheimer's disease (mental disorder) using the Caputo derivative to accurately capture long term memory and hereditary effects in neurodegeneration. The mathematical model incorporates key pathological constituents including neurons, amyloid beta (\n                    <jats:italic>A<\/jats:italic>\n                    <jats:sub>\u03b2<\/jats:sub>\n                    ), tau proteins and microglial responses, allowing detailed simulation of their dynamic interactions. Fundamental properties of the model, including positivity, boundedness, invariant regions and equilibrium points, are rigorously analyzed to ensure biological feasibility. Sensitivity analysis identifies amyloid toxicity as the most influential driver of neuronal loss underscoring its central role in AD progression. Furthermore, a Physics Informed Neural Network (PINN) is developed to approximate system dynamics from noisy observations while ensuring compliance with biological and physical constraints. Compared to standard neural networks the PINN exhibits superior accuracy and robustness especially under data scarcity. By integrating fractional calculus, optimal control and machine learning, this work advances computational modeling of Alzheimer's disease and offers insights into therapeutic optimization.\n                  <\/jats:p>","DOI":"10.3389\/fninf.2026.1748481","type":"journal-article","created":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T06:54:24Z","timestamp":1771397664000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Physics Informed Neural Network (PINN) framework for fractional order modeling of Alzheimer's disease"],"prefix":"10.3389","volume":"20","author":[{"given":"Adnan","family":"Mehmood","sequence":"first","affiliation":[{"name":"CEME, National University of Sciences and Technology (NUST)","place":["Islamabad, Pakistan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Farman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mathematics Research Center, Near East University","place":["Northern Cyprus, T\u00fcrkiye"]},{"name":"Research Center of Applied Mathematics, Khazar University","place":["Baku, Azerbaijan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farkhanda","family":"Afzal","sequence":"additional","affiliation":[{"name":"Military College of Signals (MCS), National University of Sciences and Technology (NUST)","place":["Islamabad, Pakistan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University","place":["Al Kharj, Saudi Arabia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed Altaf","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, College of Computer Engineering & Sciences, Prince Sattam Bin Abdulaziz University","place":["Al Kharj, Saudi Arabia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Hafez","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Quantity Surviving, INTI International University Colleges","place":["Nilai, Malaysia"]},{"name":"Faculty of Management","place":["Shinawatra, Pathum Thani, Thailand"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2026,2,18]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"225","DOI":"10.3390\/fractalfract9040225","article-title":"Enhanced numerical solutions for fractional PDEs using Monte Carlo PINNs coupled with cuckoo search optimization","volume":"9","author":"Ahmad","year":"2025","journal-title":"Fractal Fract"},{"key":"B2","doi-asserted-by":"publisher","first-page":"8997302","DOI":"10.1155\/2024\/8997302","article-title":"Fractional-order epidemic model for measles infection","volume":"2024","author":"Akuka","year":"2024","journal-title":"Scientifica"},{"key":"B3","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s12064-025-00448-5","article-title":"A semi-analytical approach and theoretical investigation to multi-dimensional DNA models","volume":"144","author":"Ali","year":"","journal-title":"Theory Biosci"},{"key":"B4","doi-asserted-by":"publisher","first-page":"2478","DOI":"10.1108\/EC-04-2025-0324","article-title":"Solutions of nonlinear Murray equation for blood flow in vessels by Laplace-residual power series","volume":"42","author":"Ali","year":"","journal-title":"Eng. 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