Browsing by Author "Yang, Xiao-Jun"

Now showing 1 - 20 of 53

Citation Count: Yang, Yong-Ju; Baleanu, Dumitru; Yang, Xiao-Jun, "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators", Abstract and Applied Analysis, (2013)
A Local Fractional Variational Iteration Method for Laplace Equation Within Local Fractional Operators
(Hindawi LTD, 2013) Yang, Yong-Ju; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
he local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.
Citation Count: Yang, Xiao-Jun...et al. (2017). "A new fractional derivative involving the normalized sinc function without singular kernel", Europan Physical Journal Special-Topic, Vol.226, No.16-18, pp.3567-3575.
A new fractional derivative involving the normalized sinc function without singular kernel
(Springer Heidelberg, 2017) Yang, Xiao-Jun; Gao, Feng; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
In 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.
Citation Count: Ma, Xiao-Jing...et al. (2018). "A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations", Mathematical Problems In Engineering, (2018)
A New Neumann Series Method for Solving A Family of Local Fractional Fredholm and Volterra Integral Equations
(Hindawi LTD, 2013) Ma, Xiao-Jing; Srivastava, H. M.; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.
Citation Count: Yang, Xiao-Jun...et al. (2016). "A new numerical technique for local fractional diffusion equation in fractal heat transfer", Journal of Nonlinear Sciences and Applications, Vol. 9, No. 10, pp. 5621-5628.
A new numerical technique for local fractional diffusion equation in fractal heat transfer
(Int Scientific Research Publications, 2016) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Gao, Feng; 56389
In 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.
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M. (2021). "Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics", in Methods of Mathematical Modelling and Computation for Complex Systems, Vol. 373, pp. 105-133.
Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics
(2021) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; 56389
In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics.
Citation Count: Srivastava, H.M...et al. (2015). "Advances On Integrodifferential Equations and Transforms", Abstract and Applied Analysis, Vol. 2015.
Advances On Integrodifferential Equations and Transforms
(Hindawi Publishing Corporation, 2015) Srivastava, H. M.; Yang, Xiao-Jun; Baleanu, Dumitru; Nieto, Juan J.; Hristov, Jordan,; 56389
Citation Count: Yang, Yong-Ju; Baleanu, Dumitru; Yang, Xiao-Jun, "Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method",Advances In Mathematical Physics, (2013)
Analysis of Fractal Wave Equations By Local Fractional Fourier Series Method
(Hindawi Publishing Corporation, 2013) Yang, Yong-Ju; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
The fractal wave equations with local fractional derivatives are investigated in this paper. The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.
Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives
(Elsevier Science, 2013) Yang, Xiao-Jun; Srivastava, H. M.; Baleanu, Dumitru; He, Ji-Huan; 56389
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems. (c) 2013 Published by Elsevier B.V.
Citation Count: Rahmat, Mohamad Rah Segi; Baleanu, Dumitru; Yang, Xiao-Jun (2015). "Cantor-type spherical-coordinate Method for Differential Equations within Local Fractional Derivatives", Fractional Dynamics, pp. 231-242.
Cantor-type spherical-coordinate Method for Differential Equations within Local Fractional Derivatives
(2015) Rahmat, Mohamad Rah Segi; Baleanu, Dumitru; Yang, Xiao-Jun; 56389
In this article, we utilize the Cantor-type spherical coordinate method to investigate a family of local fractional differential operators on Cantor sets. Some examples are discussed to show the capability of this method for the damped wave, Helmholtz and heat conduction equations defined on Cantor sets. We show that it is a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type spherical-coordinate systems.
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Coordinate systems of Cantor-type cylindrical and Cantor-type spherical coordinates", pp. 213-221, (2016).
Coordinate systems of Cantor-type cylindrical and Cantor-type spherical coordinates
(Elsevier Science BV, 2016) Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, Hori Mohan; 56389
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Coupling the local fractional Laplace transform with analytic methods", Local Fractional Integral Transforms and Their Applications, pp. 179-196, (2016).
Coupling the local fractional Laplace transform with analytic methods
(Elsevier Science LTD, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, Hori Mohan; 56389
Citation Count: Su, Wei-Hua...et al. (2013). "Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method", Fixed Point Theory and Applications.
Damped Wave Equation and Dissipative Wave Equation In Fractal Strings Within the Local Fractional Variational Iteration Method
(Springer International Publishing AG, 2013) Su, Wei-Hua; Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein; 56389
In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions.
Citation Count: Golmankhaneh, A.K., Yang, X.J., Baleanu, D. (2015). Einstein field equations within local fractional calculus. Romanian Journal of Physics, 60(1-2), 22-31.
Einstein field equations within local fractional calculus
(Editura Acad Romane, 2015) Golmankhaneh, Alireza K.; Yang, Xiao-Jun; Baleanu, Dumitru
In this paper, we introduce the local fractional Christoffel index symbols of the first and second kind. The divergence of a local fractional contravariant vector and the curl of local fractional covariant vector are defined. The fractional intrinsic derivative is given. The local fractional Riemann-Christoffel and Ricci tensors are obtained. Finally, the Einstein tensor and Einstein field are generalized by involving the fractional derivatives. Illustrative examples are presented
Euler-Lagrange Equatıons On Cantor Sets
(Amer Soc Mechanical Engineers, 2014) Baleanu, Dumitru; Yang, Xiao-Jun; 56389
In this manuscript, we investigated the Euler-Lagrange equations on Cantor sets within the local fractional operators. To illustrate the proposed method two examples are presented.
Citation Count: Exact Traveling-Wave Solution For Local Fractional Boussinesq Equation in Fractal Domain. (2017) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru, Fractals-Complex Geometry Patterns And Scaling in Nature And Society, 25(4)
Exact Traveling-Wave Solution For Local Fractional Boussinesq Equation In Fractal Domain
(World Scientific Publ CO PTE LTD, 2017) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; 56389
The 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.
Citation Count: Yang, X.H...et al. (2015). Fractal boundary value problems for integral and differential equations with local fractional operators. Thermal Science, 19(3), 959-966. http://dx.doi.org/10.2298/TSCI130717103Y
Fractal boundary value problems for integral and differential equations with local fractional operators
(Vinca Inst Nuclear Sci., 2015) Yang, Xiao-Jun; Baleanu, Dumitru; Lazaveric, Mihailo P.; Cajic, Milan S.
In the present paper we investigate the fractal boundary value problems for the Fredholm and Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results
Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws
(Hindawi LTD, 2014) Wang, Long-Fei; Yang, Xiao-Jun; Baleanu, Dumitru; Cattani, Carlo; Zhao, Yang; 56389
We suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus.
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru, "FRACTAL HEAT CONDUCTION PROBLEM SOLVED BY LOCAL FRACTIONAL VARIATION ITERATION METHOD", Thermal Science, Vol. 17, No. 2, ppi 625-628, (2013)
Fractal Heat Conduction Problem Solved By Local Fractional Variation Iteration Method
(Vinca Inst Nuclear Sci, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; 56389
This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.
Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator
(Springer Open, 2013) Su, Wei-Hua; Yang, Xiao-Jun; Jafari, H.; Baleanu, Dumitru; 56389
This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.
Citation Count: Yang, Xiao-Jun; Srivastava, H.M.; Baleanu, Dumitru (2015). "Initial-boundary value problems for local fractional laplace equation arising in fractal electrostatics", Journal of Applied Nonlinear Dynamics, Vol. 4, No. 4, pp. 349-356.
Initial-boundary value problems for local fractional laplace equation arising in fractal electrostatics
(2015) Yang, Xiao-Jun; Srivastava, H.M.; Baleanu, Dumitru; 56389
The initial-boundary value problems for the local fractional Laplace equation, which arises in fractal electrostatics, are investigated in this article. The non-differentiable solutions with different initial and boundary conditions are obtained by using the local fractional series expansion method. © 2015 L & H Scientific Publishing, LLC.