WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 34Citation - Scopus: 30New Solutions of the Transport Equations in Porous Media Within Local Fractional Derivative(Editura Acad Romane, 2016) Zhang, Yu; Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; MatematikIn this manuscript we use the series expansion method within local fractional derivative to obtain the solutions of both homogeneous and non-homogeneous transport equations. The new reported solutions are able to describe more efficiently the behavior of solutions of the transport phenomena in porous media.Article Citation - WoS: 19Citation - Scopus: 18New Results for Multidimensional Diffusion Equations in Fractal Dimensional Space(Editura Acad Romane, 2016) Ma, Min; Baleanu, Dumitru; Baleanu, Dumitru; Gasimov, Yusif S.; Yang, Xiao-Jun; MatematikThe multidimensional diffusion equations in fractal dimensional space started to play an important role in physics. In this paper we present the analytical solutions of the multidimensional diffusion equations in fractal dimensional spaces by using the method of separation of variables. The graphs of the exact solutions are presented and the accuracy and efficiency of the approach are revealed for a class of local fractional partial differential equations.Article Citation - WoS: 34Citation - Scopus: 36New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space(Editura Acad Romane, 2017) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Gao, Feng; MatematikWe consider the local fractional Klein Gordon equation and Helmholtz equation in (1+1) fractal dimensional space. The local fractional Laplace series expansion method is used to solve the local fractional partial differential equations in fractal dimensional space. We present the non differentiable analytical solutions and the corresponding graphs. The obtained results illustrate the accuracy and efficiency of this approach to local fractional partial differential equations.Article Citation - WoS: 32A New Numerical Technique for Local Fractional Diffusion Equation in Fractal Heat Transfer(int Scientific Research Publications, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Gao, Feng; Yang, Xiao-JunIn this paper, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer. (C) 2016 All rights reserved.Article Citation - WoS: 17Citation - Scopus: 16On Local Fractional Operators View of Computational Complexity Diffusion and Relaxation Defined on Cantor Sets(Vinca inst Nuclear Sci, 2016) Zhang, Zhi-Zhen; Machado, J. A. Tenreiro; Yang, Xiao-Jun; Baleanu, DumitruThis paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with Mittag-Leffler and exponential decay defined on Cantor sets are calculated. Comparative results with other versions of the local fractional derivatives are discussed.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: 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.Conference Object Citation - WoS: 16Citation - Scopus: 16Observing Diffusion Problems Defined on Cantor Sets in Different Co-Ordinate Systems(Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Baleanu, Mihaela-Cristina; Yang, Xiao-JunIn this paper, the 2-D and 3-D diffusions defined on Cantor sets with local fractional differential operator were discussed in different co-ordinate systems. The 2-D diffusion in Cantorian co-ordinate system can be converted into the symmetric diffusion defined on Cantor sets. The 3-D diffusions in Cantorian co-ordinate system can be observed in the Cantor-type cylindrical and spherical co-ordinate methods.