Ullah, InayatUllah, AmanAhmad, ShabirIkramullahAkgül, Ali2024-12-242024-12-2420232349-5103https://doi.org10.1007/s40819-023-01498-3https://hdl.handle.net/20.500.12604/4011The objective of this paper is to look the solution of the ocean oil equations under the three different fractional operators. We analyze the fractional ocean oil equation in one dimension using the Caputo fractional derivative. Then, using the Caputo–Fabrizio derivative, we investigate the same ocean oil equation. Finally, the Atangana–Baleanu derivative is applied to the same problem. In comparison to other analytical approaches, the Laplace transform (LT) is an easy and efficient method which has a good convergence rate for the precise solution. As a result, we employ the LT to achieve the suggested equation’s series solution. To explore the efficiency and validity of the suggested method, we present two examples of the provided equation. The error analysis of is carried out through computationally and graphically. The comparison between different Caputo, CF and ABC ocean oil equation is provided through numeric data and graphs. Finally, we offer a conclusion as well as a physical explanation of the figures. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.eninfo:eu-repo/semantics/closedAccessAtangana–Baleanu operatorCaputo operatorCaputo–Fabrizio operatorOcean oil equationArticle93Q22-s2.0-8515404129110.1007/s40819-023-01498-3