WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 118Citation - Scopus: 132Novel Fractional-Order Lagrangian To Describe Motion of Beam on Nanowire(Polish Acad Sciences inst Physics, 2021) Godwe, E.; Erturk, V. S.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A.Our aim in this research is to investigate the motion of a beam on an internally bent nanowire by using the fractional calculus theory. To this end, we first formulate the classical Lagrangian which is followed by the classical Euler-Lagrange equation. Then, after introducing the generalized fractional Lagrangian, the fractional Euler-Lagrange equation is provided for the motion of the considered beam on the nanowire. An efficient numerical scheme is introduced for implementation and the simulation results are reported for different fractional-order values and various initial settings. These results indicate that the fractional responses approach the classical ones as the fractional order goes to unity. In addition, the fractional Euler-Lagrange equation provides a flexible model possessing more information than the classical description the fact that leads to a considerably better evaluation of the hidden features of the real system under investigation.Article Citation - WoS: 13Citation - Scopus: 14A Generalisation of the Malgrange-Ehrenpreis Theorem To Find Fundamental Solutions To Fractional Pdes(Univ Szeged, Bolyai institute, 2017) Fernandez, Arran; Baleanu, DumitruWe present and prove a new generalisation of the Malgrange-Ehrenpreis theorem to fractional partial differential equations, which can be used to construct fundamental solutions to all partial differential operators of rational order and many of arbitrary real order. We demonstrate with some examples and mention a few possible applications.Article Citation - WoS: 41Citation - Scopus: 46Fractional Variational Principles With Delay Within Caputo Derivatives(Pergamon-elsevier Science Ltd, 2010) Jarad, Fahd; Abdeljawad (Maraaba), Thabet; Baleanu, Dumitru; Abdeljawad , ThabetIn this paper we investigate the fractional variational principles within Caputo derivatives in the presence of delay derivatives. The corresponding Euler-Lagrange equations are obtained for the case of one dependent variable. A generalization to it dependent variables is obtained. Physical example is analyzed in detail.