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: 42Citation - Scopus: 49An Efficient Technique for Solving the Space-Time Fractional Reaction-Diffusion Equation in Porous Media(Elsevier, 2020) Kumar, Sachin; Gomez-Aguilar, J. F.; Baleanu, D.; Pandey, PrashantIn this paper, we obtained the approximate numerical solution of space-time fractional-order reaction-diffusion equation using an efficient technique homotopy perturbation technique using Laplace transform method with fractional-order derivatives in Caputo sense. The solution obtained is very useful and significant to analyze the many physical phenomenons. The present technique demonstrates the coupling of the homotopy perturbation technique and Laplace transform using He's polynomials for finding the numerical solution of various non-linear fractional complex models. The salient features of the present work are the graphical presentations of the approximate solution of the considered porous media equation for different particular cases and reflecting the presence of reaction terms presented in the equation on the physical behavior of the solute profile for various particular cases.Article Citation - WoS: 15Citation - Scopus: 17Fractional Dynamics of an Erbium-Doped Fiber Laser Model(Springer, 2019) Saad, K. M.; Baleanu, D.; Gomez-Aguilar, J. F.In this paper we investigate the model of the time-fractional dynamics of an erbium-doped fiber laser model (TFDEFL) with Liouville-Caputo (LC), Caputo-Fabrizio-Caputo (CFC) and Atangana-Baleanu-Caputo (ABC) time-fractional derivatives. We employ the homotopy analysis transform method (HATM) to calculate approximate solutions for the TFDEFL model. This method gives the solution in the form of a rapidly convergent series that can ensure the convergence in solving the resultant series. We study the convergence analysis of HATM by computing the interval of convergence through the h-curves, the residual error function and the average residual error, respectively. We also show the effectiveness and accuracy of this method by comparing the approximate solutions based upon the LC, CFC and ABC time-fractional derivatives.