Browsing by Author "Yang, Xiao-Jun"

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The Analogues of Trigonometric Functions Defined on Cantor Sets
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 42
Citation - Scopus: 66
Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method
(Hindawi Ltd, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Yang, Yong-Ju; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 73
Citation - Scopus: 98
Anomalous Diffusion Models With General Fractional Derivatives Within the Kernels of the Extended Mittag-Leffler Type Functions
(Editura Acad Romane, 2017) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; Baleanu, Dumitru; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper addresses the new general fractional derivatives (GFDs) involving the kernels of the extended Mittag-Leffler type functions (MLFs). With the aid of the GFDs in the MLF kernels, the mathematical models for the anomalous diffusion of fractional order are analyzed and discussed. The proposed formulations are also used to describe complex phenomena that occur in heat transfer.
Citation - WoS: 105
Citation - Scopus: 111
Approximate Solutions for Diffusion Equations on Cantor Space-Time
(Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Zhong, Wei-Ping; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
Citation - WoS: 147
Citation - Scopus: 154
Cantor-Type Cylindrical-Coordinate Method for Differential Equations With Local Fractional Derivatives
(Elsevier Science Bv, 2013) Srivastava, H. M.; He, Ji-Huan; Baleanu, Dumitru; Yang, Xiao-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Cantor-type spherical-coordinate Method for Differential Equations within Local Fractional Derivatives
(2015) Rahmat, Mohamad Rah Segi; Baleanu, Dumitru; Yang, Xiao-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 1
Citation - Scopus: 1
Cantor-Type Spherical-Coordinate Method for Differential Equations Within Local Fractional Derivatives
(de Gruyter Open Ltd, 2015) Rahmat, Mohamad Rah Segi; Baleanu, Dumitru; Yang, Xiao-Jun; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Coordinate Systems of Cantor-Type Cylindrical and Cantor-Type Spherical Coordinates
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Coupling the Local Fractional Laplace Transform With Analytic Methods
(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 52
Citation - Scopus: 58
Damped Wave Equation and Dissipative Wave Equation in Fractal Strings Within the Local Fractional Variational Iteration Method
(Springer international Publishing Ag, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein; Su, Wei-Hua; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. MSC: 74H10, 35L05, 28A80.
Citation - WoS: 14
Citation - Scopus: 9
Einstein Field Equations Within Local Fractional Calculus
(Editura Acad Romane, 2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Yang, Xiao-Jun; Baleanu, D.; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - Scopus: 3
Euler-Lagrange Equations on Cantor Sets
(Amer Soc Mechanical Engineers, 2014) Baleanu, Dumitru; Yang, Xiao-Jun; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Euler-Lagrange Equatıons On Cantor Sets
(Amer Soc Mechanical Engineers, 2014) Baleanu, Dumitru; Yang, Xiao-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 179
Exact 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-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 29
Exact Travelling Wave Solutions for Local Fractional Partial Differential Equations in Mathematical Physics
(Springer international Publishing Ag, 2019) Yang, Xiao-Jun; Gao, Feng; Machado, J. A. Tenreiro; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 75
Citation - Scopus: 83
Fractal Boundary Value Problems for Integral and Differential Equations With Local Fractional Operators
(Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Lazarevic, Mihailo P.; Cajic, Milan S.; Yang, Xiao-Jun; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 15
Citation - Scopus: 26
Fractal Dynamical Model of Vehicular Traffic Flow Within the Local Fractional Conservation Laws
(Hindawi Ltd, 2014) Yang, Xiao-Jun; Baleanu, Dumitru; Cattani, Carlo; Zhao, Yang; Wang, Long-Fei; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 237
Citation - Scopus: 254
Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method
(Vinca inst Nuclear Sci, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.
Citation - WoS: 50
Citation - Scopus: 63
Fractional Complex Transform Method for Wave Equations on Cantor Sets Within Local Fractional Differential Operator
(Springer, 2013) Yang, Xiao-Jun; Jafari, H.; Baleanu, Dumitru; Su, Wei-Hua; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 4
Introduction To Local Fractional Derivative and Integral Operators
(Academic Press Ltd-elsevier Science Ltd, 2016) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-Jun; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi