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

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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.date.accessioned 2022-04-20T12:01:56Z
dc.date.available 2022-04-20T12:01:56Z
dc.date.issued 2021
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. tr_TR
dc.identifier.issn 0170-4214
dc.identifier.uri http://hdl.handle.net/20.500.12416/5403
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. © 2021 John Wiley & Sons, Ltd. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1002/mma.7251 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Exact Solutions tr_TR
dc.subject Extended Unified Method tr_TR
dc.subject Non-Autonomous Fokker–Planck Equation tr_TR
dc.subject Reduction of Fractional Derivatives tr_TR
dc.title Exact solutions of the fractional time-derivative Fokker–Planck equation: A novel approach tr_TR
dc.type conferenceObject tr_TR
dc.relation.journal Mathematical Methods in the Applied Sciences tr_TR
dc.contributor.authorID 56389 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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