Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 7About Fractional Calculus of Singular Lagrangians(Fuji Technology Press Ltd, 2005) Baleanu, DumitruIn this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.Article Citation - WoS: 1Citation - Scopus: 1Fractional Heat Equation Optimized by a Chaotic Function(Vinca inst Nuclear Sci, 2021) Wazi, Mayada T.; Baleanu, Dumitru; Al-Saidi, Nadia; Ibrahim, Rabha W.In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.Article Citation - WoS: 2Citation - Scopus: 3Conformable Differential Operators for Meromorphically Multivalent Functions(de Gruyter Poland Sp Z O O, 2021) Baleanu, Dumitru; Jahangiri, Jay M.; Ibrahim, Rabha W.We define a conformable diff-integral operator for a class of meromorphically multivalent functions. We show that this conformable operator adheres to the semigroup property. We then use the subordination properties to prove inclusion conditions, sufficienrt inclusion conditions and convolution properties for this class of conformable operators.Article Citation - WoS: 12Citation - Scopus: 12Analysis of Fractional Non-Linear Diffusion Behaviors Based on Adomian Polynomials(Vinca inst Nuclear Sci, 2017) Baleanu, Dumitru; Luo, Wei-Hua; Wu, Guo-ChengA time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.