{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T04:52:21Z","timestamp":1773895941173,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T00:00:00Z","timestamp":1743120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>This study introduces a novel one-dimensional Fractional Time\u2013Space Stochastic Advection\u2013Diffusion Equation that revolutionizes the modeling of moisture transport within atmospheric boundary layers adjacent to oceanic surfaces. By synthesizing fractional calculus, advective transport mechanisms, and pink noise stochasticity, the proposed model captures the intricate interplay between temporal memory effects, non-local turbulent diffusion, and the correlated-fluctuations characteristic of complex ocean\u2013atmosphere interactions. The framework employs the Caputo fractional derivative to represent temporal persistence and the fractional Laplacian to model non-local turbulent diffusion, and incorporates a stochastic term with a 1\/f power spectral density to simulate environmental variability. An efficient numerical solution methodology is derived utilizing complementary Fourier and Laplace transforms, which elegantly converts spatial fractional operators into algebraic expressions and yields closed-form solutions via Mittag\u2013Leffler functions. This method\u2019s application to a benchmark coastal domain demonstrates that stronger advection significantly increases the spatial extent of conditions exceeding fog formation thresholds, revealing advection\u2019s critical role in moisture transport dynamics. Numerical simulations demonstrate the model\u2019s capacity to reproduce both anomalous diffusion phenomena and realistic stochastic variability, while convergence analysis confirms the numerical scheme\u2019s robustness against varying noise intensities. This integrated fractional stochastic framework substantially advances atmospheric moisture modeling capabilities, with direct applications to meteorological forecasting, coastal climate assessment, and environmental engineering.<\/jats:p>","DOI":"10.3390\/fractalfract9040211","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T13:36:49Z","timestamp":1743169009000},"page":"211","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Fractional Time\u2013Space Stochastic Advection\u2013Diffusion Equation for Modeling Atmospheric Moisture Transport at Ocean\u2013Atmosphere Interfaces"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4957-9028","authenticated-orcid":false,"given":"Behrouz Parsa","family":"Moghaddam","sequence":"first","affiliation":[{"name":"Department of Mathematics, La.C., Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3376-7238","authenticated-orcid":false,"given":"Mahmoud A.","family":"Zaky","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio Mendes","family":"Lopes","sequence":"additional","affiliation":[{"name":"LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8262-1369","authenticated-orcid":false,"given":"Alexandra","family":"Galhano","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias Naturais, Engenharias e Tecnologias, Universidade Lus\u00f3fona-CUP, Rua Augusto Rosa 24, 4000-098 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,28]]},"reference":[{"key":"ref_1","first-page":"036601","article-title":"Approximate solutions of the advection-diffusion equation for spatially variable flows","volume":"34","author":"Sun","year":"2022","journal-title":"Phys. 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