{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T04:41:21Z","timestamp":1776746481974,"version":"3.51.2"},"reference-count":39,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T00:00:00Z","timestamp":1776643200000},"content-version":"vor","delay-in-days":109,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP2\/305\/46"],"award-info":[{"award-number":["RGP2\/305\/46"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:p>\n                    The free convective flow of heat transport with nanofluids over a plate must be studied in order to enhance thermal technologies and increase the efficiency of heat transfer in engineering system. The present article introduces the study of\n                    <jats:italic>T<\/jats:italic>\n                    <jats:italic>i<\/jats:italic>\n                    <jats:italic>o<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    and\n                    <jats:italic>C<\/jats:italic>\n                    <jats:italic>o<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    <jats:italic>O<\/jats:italic>\n                    <jats:sub>4<\/jats:sub>\n                    nanoparticles with the base fluid of\n                    <jats:italic>C<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    <jats:italic>H<\/jats:italic>\n                    <jats:sub>8<\/jats:sub>\n                    <jats:italic>O<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    . Heat transfer on Casson with the multiple effects is taken into account. This new research presents an innovative approach to studying how mass transport and heat transfer interact over a plate. The core of the problem involves complex mathematical equations called fractional partial differential equations, which are difficult to solve using traditional methods. Instead of using the standard mathematical techniques, the researchers took an artificial neural network (ANN), a type of Artificial Intelligence, and used it to solve these equations. The ANN was trained by the Levenberg\u2013Marquadrt backpropagation algorithm, which is a sophisticated optimization algorithm. The required training data were created analytically (which means precisely calculated) using the Laplace transform method. The data were divided up with 70% for the training of the primary and 15% for checking the generalization capacity of the model and the other 15% for validation. The most significant achievement of this work is the successful combining of the power of fractional calculus (for the modeling of the transport processes in detail, strictly nonjust behaving) with AIAN (neural network)\u2010based optimization (for efficient and accurate solution). This provides a credible and efficient means of modeling and ultimately optimizing heat transfer in state\u2010of\u2010the\u2010art nanofluid based engineering systems.\n                  <\/jats:p>","DOI":"10.1155\/cplx\/7826939","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T04:05:36Z","timestamp":1776744336000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Active and Passive Control of Nanofluid Heat Transfer via Fractional Operators and Neural Networks"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9730-645X","authenticated-orcid":false,"given":"Muhammad","family":"Ramzan","sequence":"first","affiliation":[]},{"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[]},{"given":"Mohammed Kbiri","family":"Alaoui","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1046-7064","authenticated-orcid":false,"given":"Shajar","family":"Abbas","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2026,4,20]]},"reference":[{"key":"e_1_2_15_1_2","article-title":"Thermal Performance of MHD Nanofluid Flow Over a Stretching Sheet due to Viscous Dissipation","author":"Mishra A.","year":"2020","journal-title":"Joule Heating and Thermal Radiation, International Journal applied and computational Math."},{"key":"e_1_2_15_2_2","article-title":"Hydrothermal Performance of Hybrid Nanofluid Flow Over an Exponentially Stretching Sheet Influenced by Gyrotactic Microorganisms: A Comparative Evaluation of Yamada-Ota and Xue Models","volume":"4","author":"Mishra A.","year":"2025","journal-title":"Numerical Heat Transfer Part A"},{"key":"e_1_2_15_3_2","doi-asserted-by":"crossref","DOI":"10.1016\/j.nanoso.2025.101515","article-title":"Thermal-Flow Characteristics of an Ellis Hybrid Nanofluid Containing polytetrafluoroethylene-SWCNTs over a stretching\/shrinking Cylinder with Slip Effect","author":"Mishra A.","year":"2025","journal-title":"Nano-Structures & Nano-Objects"},{"key":"e_1_2_15_4_2","doi-asserted-by":"crossref","DOI":"10.1007\/s12043-025-02952-1","article-title":"Performance Analysis of the Radiative Reiner\u2013Philippoff Hybrid Nanofluid Flow Over a Stretching\/Shrinking Sheet Under the Effect of Suction","author":"Mishra A.","year":"2025","journal-title":"Pramana\u2014Journal of Physics"},{"key":"e_1_2_15_5_2","article-title":"Simulation of SWCNTs-MWCNTs\/Water-Based MHD Hybrid Nanofluid Flow Over an Exponentially Stretching Sheet Using Xue Model","author":"Mishra A.","year":"2024","journal-title":"Ricerche di Matematica"},{"key":"e_1_2_15_6_2","doi-asserted-by":"crossref","DOI":"10.1016\/j.heliyon.2023.e21453","article-title":"Development of Machine Learning Algorithm for Assessment of Heat Transfer of Ternary Hybrid Nanofluid Flow Towards Three Different Geometries: Case of Artificial Neural Network","author":"Mishra A.","year":"2023","journal-title":"Heliyon"},{"key":"e_1_2_15_7_2","doi-asserted-by":"crossref","DOI":"10.1142\/8180","volume-title":"Fractional Calculus: Models and Numerical Methods","author":"Baleanu D.","year":"2012"},{"key":"e_1_2_15_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.08.018"},{"key":"e_1_2_15_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.08.002"},{"key":"e_1_2_15_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.7293"},{"key":"e_1_2_15_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2016.11.014"},{"key":"e_1_2_15_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2022.01.067"},{"key":"e_1_2_15_13_2","first-page":"1","article-title":"Cobalt\u2014Properties\u2014Price\u2014Applications\u2014Production","volume":"2","author":"Connor N.","year":"2020","journal-title":"Material Properties"},{"key":"e_1_2_15_14_2","doi-asserted-by":"publisher","DOI":"10.9790\/1813-0604010813"},{"key":"e_1_2_15_15_2","first-page":"145","article-title":"MHD Free Convective Flow of Jeffrey Fluid With Prabhakar Like Fractional Model Subject to Generalizedthermal Transport","volume":"1","author":"Siddique I.","year":"2023","journal-title":"Scientific Reports"},{"key":"e_1_2_15_16_2","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.jppr.2015.04.001","article-title":"On Linearization Method to MHD Boundary Layer Convective Heat Transfer With Flow Pressure Gradient","volume":"4","author":"Ahmed M. 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