Saima Rashid , Mohammed K.A. Kaabar , Ali Althobaiti , M.S. Alqurashi
{"title":"Constructing analytical estimates of the fuzzy fractional-order Boussinesq model and their application in oceanography","authors":"Saima Rashid , Mohammed K.A. Kaabar , Ali Althobaiti , M.S. Alqurashi","doi":"10.1016/j.joes.2022.01.003","DOIUrl":null,"url":null,"abstract":"<div><p>The main idea of this article is the investigation of atmospheric internal waves, often known as gravity waves. This arises within the ocean rather than at the interface. A shallow fluid assumption is illustrated by a series of nonlinear partial differential equations in the framework. Because the waves are scattered over a wide geographical region, this system can precisely replicate atmospheric internal waves. In this research, the numerical solutions to the fuzzy fourth-order time-fractional Boussinesq equation (BSe) are determined for the case of the aquifer propagation of long waves having small amplitude on the surface of water from a channel. The novel scheme, namely the generalized integral transform (proposed by H. Jafari [35]) coupled with the Adomian decomposition method (GIADM), is used to extract the fuzzy fractional BSe in <span><math><mrow><mi>R</mi><mo>,</mo><mspace></mspace><msup><mi>R</mi><mi>n</mi></msup></mrow></math></span> and <span><math><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mi>t</mi><mi>h</mi><mo>)</mo></mrow></math></span>-order including <span><math><mrow><mi>g</mi><mi>H</mi></mrow></math></span>-differentiability. To have a clear understanding of the physical phenomena of the projected solutions, several algebraic aspects of the generalized integral transform in the fuzzy Caputo and Atangana-Baleanu fractional derivative operators are discussed. The confrontation between the findings by Caputo and ABC fractional derivatives under generalized Hukuhara differentiability are presented with appropriate values for the fractional order and uncertainty parameters <span><math><mrow><mi>℘</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> were depicted in diagrams. According to proposed findings, hydraulic engineers, being analysts in drainage or in water management, might access adequate storage volume quantity with an uncertainty level.</p></div>","PeriodicalId":48514,"journal":{"name":"Journal of Ocean Engineering and Science","volume":null,"pages":null},"PeriodicalIF":13.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Ocean Engineering and Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468013322000158","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MARINE","Score":null,"Total":0}
引用次数: 6
Abstract
The main idea of this article is the investigation of atmospheric internal waves, often known as gravity waves. This arises within the ocean rather than at the interface. A shallow fluid assumption is illustrated by a series of nonlinear partial differential equations in the framework. Because the waves are scattered over a wide geographical region, this system can precisely replicate atmospheric internal waves. In this research, the numerical solutions to the fuzzy fourth-order time-fractional Boussinesq equation (BSe) are determined for the case of the aquifer propagation of long waves having small amplitude on the surface of water from a channel. The novel scheme, namely the generalized integral transform (proposed by H. Jafari [35]) coupled with the Adomian decomposition method (GIADM), is used to extract the fuzzy fractional BSe in and -order including -differentiability. To have a clear understanding of the physical phenomena of the projected solutions, several algebraic aspects of the generalized integral transform in the fuzzy Caputo and Atangana-Baleanu fractional derivative operators are discussed. The confrontation between the findings by Caputo and ABC fractional derivatives under generalized Hukuhara differentiability are presented with appropriate values for the fractional order and uncertainty parameters were depicted in diagrams. According to proposed findings, hydraulic engineers, being analysts in drainage or in water management, might access adequate storage volume quantity with an uncertainty level.
期刊介绍:
The Journal of Ocean Engineering and Science (JOES) serves as a platform for disseminating original research and advancements in the realm of ocean engineering and science.
JOES encourages the submission of papers covering various aspects of ocean engineering and science.