WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 182Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain(World Scientific Publ Co Pte Ltd, 2017) Tenreiro Machado, J. A.; Baleanu, Dumitru; Yang, Xiao-JunThe new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.Article Citation - WoS: 119Citation - Scopus: 130A Hybrid Computational Approach for Klein-Gordon Equations on Cantor Sets(Springer, 2017) Singh, Jagdev; Baleanu, Dumitru; Kumar, DevendraIn this letter, we present a hybrid computational approach established on local fractional Sumudu transform method and homotopy perturbation technique to procure the solution of the Klein-Gordon equations on Cantor sets. Four examples are provided to show the accuracy and coherence of the proposed technique. The outcomes disclose that the present computational approach is very user friendly and efficient to compute the nondifferentiable solution of Klein-Gordon equation involving local fractional operator.Article Citation - WoS: 148Citation - Scopus: 144Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets(Pergamon-elsevier Science Ltd, 2015) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunIn this letter, the local fractional similarity solution is addressed for the non-differentiable diffusion equation. Structuring the similarity transformations via the rule of the local fractional partial derivative operators, we transform the diffusive operator into a similarity ordinary differential equation. The obtained result shows the non-differentiability of the solution suitable to describe the properties and behaviors of the fractal content. (C) 2015 Published by Elsevier Ltd.