Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 69Citation - Scopus: 103Variational Iteration Method for Fractional Calculus - a Universal Approach by Laplace Transform(Springeropen, 2013) Baleanu, Dumitru; Wu, Guo-ChengA novel modification of the variational iteration method (VIM) is proposed by means of the Laplace transform. Then the method is successfully extended to fractional differential equations. Several linear fractional differential equations are analytically solved as examples and the methodology is demonstrated.Article Citation - WoS: 69Citation - Scopus: 68New Applications of the Variational Iteration Method - From Differential Equations To Q-Fractional Difference Equations(Springeropen, 2013) Baleanu, Dumitru; Wu, Guo-ChengThe non-classical calculi such as q-calculus, fractional calculus and q-fractional calculus have been hot topics in both applied and pure sciences. Then some new linear and nonlinear models have appeared. This study mainly concentrates on the analytical aspects, and the variational iteration method is extended in a new way to solve an initial value problem.Article Citation - WoS: 39Citation - Scopus: 43A Reliable Technique for Fractional Modified Boussinesq and Approximate Long Wave Equations(Springeropen, 2019) Prakasha, D. G.; Qurashi, M. A.; Baleanu, D.; Veeresha, P.In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology.Article Citation - WoS: 33Citation - Scopus: 33Comparative Simulations for Solutions of Fractional Sturm-Liouville Problems With Non-Singular Operators(Springeropen, 2018) Ozarslan, Ramazan; Baleanu, Dumitru; Ercan, Ahu; Bas, ErdalIn this study, we consider fractional Sturm-Liouville (S-L) problems within non-singular operators. A fractional S-L problem with exponential and Mittag-Leffler kernels is given with different versions in the Riemann-Liouville and Caputo sense. Also, we obtain representation of solutions for S-L problems by the Laplace transform and find analytical solutions of the problems. Finally, we compare the solutions of the problem with these different versions, and we also compare the solutions of the problem with exponential and Mittag-Leffler kernels together by simulation under different potentials, different orders, and different eigenvalues.