{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:54:30Z","timestamp":1777492470949,"version":"3.51.4"},"reference-count":59,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T00:00:00Z","timestamp":1680393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Fractional calculus is at this time an area where many models are still being developed, explored, and used in real-world applications in many branches of science and engineering where non-locality plays a key role. Although many wonderful discoveries have already been reported by researchers in important monographs and review articles, there is still a great deal of non-local phenomena that have not been studied and are only waiting to be explored. As a result, we can continually learn about new applications and aspects of fractional modelling. In this study, a precise and analytical method with non-singular kernel derivatives is used to solve the Caudrey\u2013Dodd\u2013Gibbon (CDG) model, a modification of the fifth-order KdV equation (fKdV). The fractional derivative is taken into account by the Caputo\u2013Fabrizio (CF) derivative and the Atangana\u2013Baleanu derivative in the Caputo sense (ABC). This model illustrates the propagation of magneto-acoustic, shallow-water, and gravity\u2013capillary waves in a plasma medium. The dynamic behaviour of the acquired solutions has been represented in a number of two- and three-dimensional figures. A number of simulations are also performed to demonstrate how the resulting solutions physically behave with respect to fractional order. The significance of the current research is that new solutions are obtained by using a strong analytical approach. Utilizing a fractional derivative operator to solve equivalent models is another benefit of this approach. The results of the present work have similar aspects to the symmetry of partial differential equations.<\/jats:p>","DOI":"10.3390\/sym15040850","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T03:32:59Z","timestamp":1680492779000},"page":"850","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["An Efficient Analytical Approach to Investigate Fractional Caudrey\u2013Dodd\u2013Gibbon Equations with Non-Singular Kernel Derivatives"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9516-1485","authenticated-orcid":false,"given":"Dowlath","family":"Fathima","sequence":"first","affiliation":[{"name":"Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0181-7552","authenticated-orcid":false,"given":"Reham A.","family":"Alahmadi","sequence":"additional","affiliation":[{"name":"Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]},{"given":"Adnan","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan"}]},{"given":"Afroza","family":"Akhter","sequence":"additional","affiliation":[{"name":"School of Advanced Science and Languages, VIT Bhopal University, Kothrikalan, Sehore 466114, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1787-5036","authenticated-orcid":false,"given":"Abdul Hamid","family":"Ganie","sequence":"additional","affiliation":[{"name":"Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,2]]},"reference":[{"key":"ref_1","first-page":"211","article-title":"New Bounds for Variables of Fractional Order","volume":"38","author":"Ganie","year":"2022","journal-title":"Pak. 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