Çankaya GCRIS Standart veritabanının içerik oluşturulması ve kurulumu Research Ecosystems (https://www.researchecosystems.com) tarafından devam etmektedir. Bu süreçte gördüğünüz verilerde eksikler olabilir.
 

Exact solutions of the fractional time-derivative Fokker–Planck equation: A novel approach

dc.authorid Abdel-Gawad, Hamdy/0000-0003-1986-2324
dc.authorid Al-Mekhlafi, Seham/0000-0003-0351-9679
dc.authorscopusid 6603752855
dc.authorscopusid 6507922829
dc.authorscopusid 56716517100
dc.authorscopusid 7005872966
dc.authorwosid Baleanu, Dumitru/B-9936-2012
dc.authorwosid Al-Mekhlafi, Seham/Aab-4858-2022
dc.authorwosid Sweilam, Nasser/Q-2175-2019
dc.contributor.author Abdel-Gawad, Hamdy I.
dc.contributor.author Sweilam, Nasser H.
dc.contributor.author Al-Mekhlafi, Seham M.
dc.contributor.author Baleanu, Dumitru
dc.contributor.authorID 56389 tr_TR
dc.contributor.other Matematik
dc.date.accessioned 2022-04-20T12:01:56Z
dc.date.available 2022-04-20T12:01:56Z
dc.date.issued 2023
dc.department Çankaya University en_US
dc.department-temp [Abdel-Gawad, Hamdy I.; Sweilam, Nasser H.] Cairo Univ, Math Dept, Fac Sci, Giza, Egypt; [Al-Mekhlafi, Seham M.] Sanaa Univ, Fac Educ, Math Dept, Sanaa, Yemen; [Baleanu, Dumitru] Cankaya Univ, Dept Math, Ankara, Turkey; [Baleanu, Dumitru] Inst Space Sci, Magurele, Romania en_US
dc.description Abdel-Gawad, Hamdy/0000-0003-1986-2324; Al-Mekhlafi, Seham/0000-0003-0351-9679 en_US
dc.description.abstract In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation (FFPE) is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together with implementing the extended unified method. On the other hand, a theorem provides the reduction of the fractional derivatives to non-autonomous ordinary derivative is given. Thus, the FFPE is reduced to non-autonomous classical ones. Some explicit solutions of the classical, fractional time-derivative Fokker-Planck equation are obtained. It is shown that the solution of the Fokker-Planck equation is bi-Gaussian's, which was not found up to date. It is found that high friction coefficient plays a significant role in lowering the standard deviation. Further, it is found that the effect of the presence of the fractional derivative prevails that of the fractal derivative. Here, the most interesting result found is that mixed-Gaussian solution is obtained. It is worthy to mention that the mixture of Gaussian's is a powerful tool in machine learning and also in the distribution of loads in networks. Further, varying the order of the fractional time derivatives results to slight effects in the probability distribution function. Also, it is shown that the mean and mean square of the velocity vary slowly. en_US
dc.description.woscitationindex Science Citation Index Expanded
dc.identifier.citation Abdel-Gawad, Hamdy I...et al. (2021). "Exact solutions of the fractional time-derivative Fokker–Planck equation: A novel approach", Mathematical Methods in the Applied Sciences. en_US
dc.identifier.doi 10.1002/mma.7251
dc.identifier.endpage 7874 en_US
dc.identifier.issn 0170-4214
dc.identifier.issn 1099-1476
dc.identifier.issue 7 en_US
dc.identifier.scopus 2-s2.0-85100544236
dc.identifier.scopusquality Q1
dc.identifier.startpage 7861 en_US
dc.identifier.uri https://doi.org/10.1002/mma.7251
dc.identifier.volume 46 en_US
dc.identifier.wos WOS:000614282700001
dc.identifier.wosquality Q1
dc.institutionauthor Baleanu, Dumitru
dc.language.iso en en_US
dc.publisher Wiley en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 3
dc.subject Exact Solutions en_US
dc.subject Extended Unified Method en_US
dc.subject Non&#8208 en_US
dc.subject Autonomous Fokker&#8211 en_US
dc.subject Planck Equation en_US
dc.subject Reduction Of Fractional Derivatives en_US
dc.title Exact solutions of the fractional time-derivative Fokker–Planck equation: A novel approach tr_TR
dc.title Exact Solutions of the Fractional Time-Derivative Fokker-Planck Equation: a Novel Approach en_US
dc.type Article en_US
dc.wos.citedbyCount 2
dspace.entity.type Publication
relation.isAuthorOfPublication f4fffe56-21da-4879-94f9-c55e12e4ff62
relation.isAuthorOfPublication.latestForDiscovery f4fffe56-21da-4879-94f9-c55e12e4ff62
relation.isOrgUnitOfPublication 26a93bcf-09b3-4631-937a-fe838199f6a5
relation.isOrgUnitOfPublication.latestForDiscovery 26a93bcf-09b3-4631-937a-fe838199f6a5

Files

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description: