{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T05:13:04Z","timestamp":1785301984504,"version":"3.55.0"},"reference-count":55,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T00:00:00Z","timestamp":1675641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Researchers","award":["PNURSP2023R27"],"award-info":[{"award-number":["PNURSP2023R27"]}]},{"name":"Khalifa University, Abu Dhabi, United Arab Emirates","award":["PNURSP2023R27"],"award-info":[{"award-number":["PNURSP2023R27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The importance of partial differential equations in physics, mathematics and engineering cannot be emphasized enough. Partial differential equations are used to represent physical processes, which are then solved analytically or numerically to examine the dynamical behaviour of the system. The new iterative approach and the Homotopy perturbation method are used in this article to solve the fractional order Fokker\u2013Planck equation numerically. The Caputo sense is used to characterize the fractional derivatives. The suggested approach\u2019s accuracy and applicability are demonstrated using illustrations. The proposed method\u2019s accuracy is expressed in terms of absolute error. The proposed methods are found to be in good agreement with the exact solution of the problems using graphs and tables. The results acquired using the given approaches are also obtained at various fractional orders of the derivative. It is observed from the graphs and tables that fractional order solutions converge to an integer solution when the fractional orders approach the integer-order of the problems. The tabular and graphical view for the given problems is obtained through Maple. The presented approaches can be applied to existing non-linear fractional partial differential equations due to their accurate, simple and straightforward implementation.<\/jats:p>","DOI":"10.3390\/sym15020430","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T04:08:07Z","timestamp":1675656487000},"page":"430","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Comparative Analysis of Fractional-Order Fokker\u2013Planck Equation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2116-7382","authenticated-orcid":false,"given":"Fatemah","family":"Mofarreh","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Asfandyar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rasool","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5775-516X","authenticated-orcid":false,"given":"Alrazi","family":"Abdeljabbar","sequence":"additional","affiliation":[{"name":"Mathematics Department, Khalifa University, Abu Dhabi 127788, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,6]]},"reference":[{"key":"ref_1","first-page":"310","article-title":"The Fengs first integral method applied to the nonlinear mKdV space-time fractional partial differential equation","volume":"62","author":"Sosa","year":"2016","journal-title":"Rev. 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