Percorrer por autor "Yang, Xiao-Jun"
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- Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operatorsPublication . Baleanu, Dumitru; Machado, J. A. Tenreiro; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-JunWe perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.
- Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent VariablesPublication . Chen, Li; Zhao, Yang; Jafari, Hossein; Machado, J. A. Tenreiro; Yang, Xiao-JunThe local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.
- Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent VariablesPublication . Chen, Li; Zhao, Yang; Jafari, Hossein; Machado, J. A. Tenreiro; Yang, Xiao-JunThe local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.
- Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysisPublication . Yang, Xiao-Jun; Baleanu, Dumitru; Machado, J. A. TenreiroIn this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.
- A New Family of the Local Fractional PDEsPublication . Yang, Xiao-Jun; Machado, J. A. Tenreiro; Nieto, Juan J.A new family of the local fractional PDEs is investigated in this article. The linear, quasi-linear, semilinear and nonlinear local fractional PDEs are presented. Furthermore, three types of the local fractional PDEs are discussed, namely, parabolic, hyperbolic and elliptic. Several examples illustrate the corresponding models in nonlinear mathematical physics.
- A new fractional derivative involving the normalized sinc function without singular kernelPublication . Yang, Xiao-Jun; Gao, Feng; Tenreiro Machado, J. A.; Baleanu, DumitruIn this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.
- A new fractional derivative without singular kernelPublication . Yang, Xiao-Jun; Srivastava, Hari M.; Machado, J. A. TenreiroIn this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.
- A new fractional operator of variable order: application in the description of anomalous diffusionPublication . Yang, Xiao-Jun; Tenreiro Machado, J. A.In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.
- A new insight into complexity from the local fractional calculus view point: modelling growths of populationsPublication . Yang, Xiao-Jun; Machado, J. A. TenreiroIn this paper, we model the growths of populations by means of local fractional calculus. We formulate the local fractionalrate equation and the local fractional logistic equation. The exact solutions of local fractional rate equation andlocal fractional logistic equation with the Mittag-Leffler function defined on Cantor sets are presented. The obtainedresults illustrate the accuracy and efficiency for modeling the complexity of linear and nonlinear population dynamics (PD).
- A new numerical technique for local fractional diffusion equation in fractal heat transferPublication . Yang, Xiao-Jun; Machado, J. A. Tenreiro; Baleanu, Dumitru; Gao, FengIn this paper, a new numerical approach, embedding the differential transform (DT) and Laplace trans- form (LT), is frstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer.