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Volumn 17, Issue 3, 2013, Pages 707-713

The yang-fourier transforms to heat-conduction in a semi-infinite fractal bar

Author keywords

Fractal bar; Heat conduction equation; Local fractional calculus; Yang Fourier transforms

Indexed keywords

CALCULATIONS; FOURIER TRANSFORMS; HEAT CONDUCTION;

EID: 84884896550     PISSN: 03549836     EISSN: None     Source Type: Journal    
DOI: 10.2298/TSCI120826074Y     Document Type: Article
Times cited : (51)

References (40)
  • 1
    • 33847309315 scopus 로고    scopus 로고
    • Theory and Applications of Fractional Differential Equations
    • Elsevier Science, Amsterdam
    • Kilbas, A.A., et al., Theory and Applications of Fractional Differential Equations, Elsevier Science, Amsterdam, 2006
    • (2006)
    • Kilbas, A.A.1
  • 2
    • 84967432140 scopus 로고    scopus 로고
    • Fractional Calculus and Waves in Linear Viscoelasticity
    • Imperial College Press, London
    • Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, London, 2010
    • (2010)
    • Mainardi, F.1
  • 3
    • 0003797958 scopus 로고    scopus 로고
    • Fractional Differential Equations
    • Academic Press, New York, USA
    • Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
    • (1999)
    • Podlubny, I.1
  • 4
    • 84855597986 scopus 로고    scopus 로고
    • Fractional Dynamics in Physics: Recent Advances
    • World Scientific, Singapore
    • Klafter, J., et al., (Eds.), Fractional Dynamics in Physics: Recent Advances, World Scientific, Singapore, 2012
    • (2012)
    • Klafter, J.1
  • 5
    • 19944362013 scopus 로고    scopus 로고
    • Hamiltonian Chaos and Fractional Dynamics
    • Oxford University Press, Oxford, UK
    • Zaslavsky, G.M., Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005
    • (2005)
    • Zaslavsky, G.M.1
  • 6
    • 0004315248 scopus 로고    scopus 로고
    • Physics of Fractal Operators
    • Springer, New York, USA
    • West, B., et al., Physics of Fractal Operators, Springer, New York, USA, 2003
    • (2003)
    • West, B.1
  • 7
    • 0003678617 scopus 로고    scopus 로고
    • Fractals and Fractional Calculus in Continuum Mechanics
    • Springer, Wiena
    • Carpinteri, A., Mainardi, F., (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Wiena, 1997
    • (1997)
    • Carpinteri, A.1    Mainardi, F.2
  • 8
    • 65049084831 scopus 로고    scopus 로고
    • Fractional Calculus Models and Numerical Methods
    • Complexity, Nonlinearity and Chaos, World Scientific, Singapore
    • Baleanu, D., et al., Fractional Calculus Models and Numerical Methods, Complexity, Nonlinearity and Chaos, World Scientific, Singapore, 2012
    • (2012)
    • Baleanu, D.1
  • 9
    • 77955895114 scopus 로고    scopus 로고
    • Heat-Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model
    • Hristov, J., Heat-Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model, Thermal Science, 14 (2010), 2, pp. 291-316
    • (2010) Thermal Science , vol.14 , Issue.2 , pp. 291-316
    • Hristov, J.1
  • 10
    • 84868622059 scopus 로고    scopus 로고
    • Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid
    • Hristov, J., Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid, Thermal Science, 16 (2012), 2, pp. 395-410
    • (2012) Thermal Science , vol.16 , Issue.2 , pp. 395-410
    • Hristov, J.1
  • 11
    • 84870906105 scopus 로고    scopus 로고
    • Transient Flow of a Generalized Second Grade Fluid Due to a Constant Surface Shear Stress: An Approximate Integral-Balance Solution
    • Hristov, J., Transient Flow of a Generalized Second Grade Fluid Due to a Constant Surface Shear Stress: An Approximate Integral-Balance Solution, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 802-809
    • (2011) Int. Rev. Chem. Eng. , vol.3 , Issue.6 , pp. 802-809
    • Hristov, J.1
  • 12
    • 84871756844 scopus 로고    scopus 로고
    • A Modified Variational Iteration Method for Solving Fractional Riccati Differential Equation by Adomian Polynomials
    • Jafari, H., et al., A Modified Variational Iteration Method for Solving Fractional Riccati Differential Equation by Adomian Polynomials, Fractional Calculus and Applied Analysis, 16 (2013), 1, pp. 109-122
    • (2013) Fractional Calculus and Applied Analysis , vol.16 , Issue.1 , pp. 109-122
    • Jafari, H.1
  • 13
    • 84874035986 scopus 로고    scopus 로고
    • Variational Iteration Method for Fractional Calculus-a Universal Approach by Laplace Transform
    • Wu, G. C., Baleanu, D., Variational Iteration Method for Fractional Calculus-a Universal Approach by Laplace Transform, Advances in Difference Equations, 2013 (2013), 1, pp. 1-9
    • (2013) Advances in Difference Equations , vol.2013 , Issue.1 , pp. 1-9
    • Wu, G.C.1    Baleanu, D.2
  • 14
    • 70349767158 scopus 로고    scopus 로고
    • Application of Variational Iteration Method to Fractional Initial-Value Problems
    • Ates, I., Yildirim, A., Application of Variational Iteration Method to Fractional Initial-Value Problems, Int. J. Nonl. Sci. Num. Sim., 10 (2009), 7, pp. 877-884
    • (2009) Int. J. Nonl. Sci. Num. Sim. , vol.10 , Issue.7 , pp. 877-884
    • Ates, I.1    Yildirim, A.2
  • 15
    • 84859427726 scopus 로고    scopus 로고
    • Solutions of the Initial Value Problem for Nonlinear Fractional Ordinary Differential Equations by the Rach-Adomian-Meyers Modified Decomposition Method
    • Duan, J. S., et al., Solutions of the Initial Value Problem for Nonlinear Fractional Ordinary Differential Equations by the Rach-Adomian-Meyers Modified Decomposition Method, Appl. Math.Comput., 218 (2012), 17, pp. 8370-8392
    • (2012) Appl. Math.Comput. , vol.218 , Issue.17 , pp. 8370-8392
    • Duan, J.S.1
  • 16
    • 77952597982 scopus 로고    scopus 로고
    • Analytical Approximate Solutions of the Fractional Convection-Diffusion Equation with Nonlinear Source Term by He's Homotopy Perturbation Method
    • Momani, S., Yildirim, A., Analytical Approximate Solutions of the Fractional Convection-Diffusion Equation with Nonlinear Source Term by He's Homotopy Perturbation Method, Int. J Comp. Math., 87 (2010), 5, pp. 1057-1065
    • (2010) Int. J Comp. Math. , vol.87 , Issue.5 , pp. 1057-1065
    • Momani, S.1    Yildirim, A.2
  • 17
    • 84872763477 scopus 로고    scopus 로고
    • Fractional Variational Homotopy Perturbation Iteration Method and Its Application to a Fractional Diffusion Equation
    • Guo, S., et al., Fractional Variational Homotopy Perturbation Iteration Method and Its Application to a Fractional Diffusion Equation, Appl. Math.Comput., 219 (2013), 11, pp. 5909-5917
    • (2013) Appl. Math.Comput. , vol.219 , Issue.11 , pp. 5909-5917
    • Guo, S.1
  • 18
    • 84875907616 scopus 로고    scopus 로고
    • A Semi-Discrete Finite Element Method for a Class of Time-Fractional Diffusion Equations
    • Sun, H. G., et al., A Semi-Discrete Finite Element Method for a Class of Time-Fractional Diffusion Equations, Phil. Trans. Royal Soc. A: 371 (2013), 1990, pp. 1471-2962
    • (2013) Phil. Trans. Royal Soc. A , vol.371 , Issue.1990 , pp. 1471-2962
    • Sun, H.G.1
  • 19
    • 84874533666 scopus 로고    scopus 로고
    • Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations
    • Article ID 587179
    • Jafari, H., et al., Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations, Abstract and Applied Analysis, 2013 (2013), Article ID 587179
    • (2013) Abstract and Applied Analysis , vol.2013
    • Jafari, H.1
  • 20
  • 21
    • 84876037987 scopus 로고    scopus 로고
    • On Convergence of Homotopy Analysis Method and its Application to Fractional integro-Differential Equations
    • Abbasbandy, S., Hashemi, M. S., On Convergence of Homotopy Analysis Method and its Application to Fractional integro-Differential Equations, Quaestiones Mathematicae, 36 (2013), 1, pp. 93-105
    • (2013) Quaestiones Mathematicae , vol.36 , Issue.1 , pp. 93-105
    • Abbasbandy, S.1    Hashemi, M.S.2
  • 22
    • 50249146464 scopus 로고    scopus 로고
    • Homotopy Analysis Method for Fractional IVPs
    • Hashim, I., et al., Homotopy Analysis Method for Fractional IVPs, Comm. Nonl. Sci. Num.Sim., 14 (2009), 3, pp. 674-684
    • (2009) Comm. Nonl. Sci. Num.Sim. , vol.14 , Issue.3 , pp. 674-684
    • Hashim, I.1
  • 23
    • 84871814483 scopus 로고    scopus 로고
    • The Finite Difference Methods for Fractional Ordinary Differential Equations
    • Li, C., Zeng, F., The Finite Difference Methods for Fractional Ordinary Differential Equations, Num. Func. Anal. Optim., 34 (2013), 2, pp. 149-179
    • (2013) Num. Func. Anal. Optim. , vol.34 , Issue.2 , pp. 149-179
    • Li, C.1    Zeng, F.2
  • 24
    • 84886793193 scopus 로고    scopus 로고
    • Analysis of Fractional Partial Differential Equations by Taylor Series Expansion
    • Demir, A., et al., Analysis of Fractional Partial Differential Equations by Taylor Series Expansion, Boundary Value Problems, 2013 (2013), 1, pp. 68-80
    • (2013) Boundary Value Problems , vol.2013 , Issue.1 , pp. 68-80
    • Demir, A.1
  • 25
    • 0001707390 scopus 로고    scopus 로고
    • Local Fractional Fokker-Planck Equation
    • Kolwankar, K. M., Gangal, A. D., Local Fractional Fokker-Planck Equation, Physical Review Letters, 80 (1998), 2, pp. 214-217
    • (1998) Physical Review Letters , vol.80 , Issue.2 , pp. 214-217
    • Kolwankar, K.M.1    Gangal, A.D.2
  • 26
    • 27744450698 scopus 로고    scopus 로고
    • Time-Space Fabric Underlying Anomalous Diffusion, Chaos
    • Chen, W., Time-Space Fabric Underlying Anomalous Diffusion, Chaos, Solitons& Fractals, 28 (2006), 4, pp. 923-929
    • (2006) Solitons& Fractals , vol.28 , Issue.4 , pp. 923-929
    • Chen, W.1
  • 27
    • 84871448093 scopus 로고    scopus 로고
    • Fractal Derivative Model for Air Permeability in Hierarchic Porous Media
    • Article ID 354701
    • Fan, J., He, J.- H., Fractal Derivative Model for Air Permeability in Hierarchic Porous Media, Abstract and Applied Analysis, 2012 (2012), Article ID 354701
    • (2012) Abstract and Applied Analysis , vol.2012
    • Fan, J.1    He, J.-H.2
  • 28
    • 65449159066 scopus 로고    scopus 로고
    • Probability Calculus of Fractional Order and Fractional Taylor's Series Application to Fokker-Planck Equation and Information of Non-Random Functions, Chaos
    • Jumarie, G., Probability Calculus of Fractional Order and Fractional Taylor's Series Application to Fokker-Planck Equation and Information of Non-Random Functions, Chaos, Solitons & Fractals, 40 (2009), 3, pp. 1428-1448
    • (2009) Solitons & Fractals , vol.40 , Issue.3 , pp. 1428-1448
    • Jumarie, G.1
  • 29
    • 77049111800 scopus 로고    scopus 로고
    • Diffusion Problems in Fractal Media Defined on Cantor Sets
    • Carpinteri, A., Sapora, A., Diffusion Problems in Fractal Media Defined on Cantor Sets, ZAMM, 90 (2010), 3, pp. 203-210
    • (2010) ZAMM , vol.90 , Issue.3 , pp. 203-210
    • Carpinteri, A.1    Sapora, A.2
  • 30
    • 84857478992 scopus 로고    scopus 로고
    • Local Fractional Functional Analysis and Its Applications
    • Asian Academic publisher Limited, Hong Kong
    • Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic publisher Limited, Hong Kong, 2011
    • (2011)
    • Yang, X.J.1
  • 31
    • 84555221318 scopus 로고    scopus 로고
    • Local Fractional Integral Transforms
    • Progress in Nonlinear Science
    • Yang, X. J., Local Fractional Integral Transforms, Progress in Nonlinear Science, 4 (2011)
    • (2011) , vol.4
    • Yang, X.J.1
  • 32
    • 84871843060 scopus 로고    scopus 로고
    • Advanced Local Fractional Calculus and Its Applications
    • World Science Publisher, New York, USA
    • Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
    • (2012)
    • Yang, X.J.1
  • 33
    • 84879315907 scopus 로고    scopus 로고
    • Fractional Complex Transform Method for Wave Equations on Cantor Sets within Local Fractional Differential Operator
    • Su,W. H., et al., Fractional Complex Transform Method for Wave Equations on Cantor Sets within Local Fractional Differential Operator, Advances in Difference Equations, 2013 (2013), 1, pp. 97-103
    • (2013) Advances in Difference Equations , vol.2013 , Issue.1 , pp. 97-103
    • Su, W.H.1
  • 34
    • 84874182595 scopus 로고    scopus 로고
    • One-Phase Problems for Discontinuous Heat Transfer in Fractal Media
    • Article ID 358473, 2013
    • Hu, M. S., et al., One-Phase Problems for Discontinuous Heat Transfer in Fractal Media, Mathematical Problems in Engineering, 2013 (2013), Article ID 358473, 2013
    • (2013) Mathematical Problems in Engineering , vol.2013
    • Hu, M.S.1
  • 35
    • 84879324154 scopus 로고    scopus 로고
    • Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method
    • Yang, X, J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
    • (2013) Thermal Science , vol.17 , Issue.2 , pp. 625-628
    • Yang, X.J.1    Baleanu, D.2
  • 36
    • 84877292735 scopus 로고    scopus 로고
    • A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators
    • Article ID 202650
    • Yang, Y., J., et al., A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis, 2013 (2013), Article ID 202650
    • (2013) Abstract and Applied Analysis , vol.2013
    • Yang, Y.J.1
  • 37
    • 84879310679 scopus 로고    scopus 로고
    • Damped Wave Equation and Dissipative Wave Equation in Fractal Strings within the Local Fractional Variational Iteration Method
    • Su,W. H., et al., Damped Wave Equation and Dissipative Wave Equation in Fractal Strings within the Local Fractional Variational Iteration Method, Fixed Point Theory and Applications, 2013 (2013), 1, pp. 89-102
    • (2013) Fixed Point Theory and Applications , vol.2013 , Issue.1 , pp. 89-102
    • Su, W.H.1
  • 38
    • 84872148874 scopus 로고    scopus 로고
    • Local Fractional Fourier Series with Application to wave Equation in Fractal Vibrating String
    • Article ID 567401
    • Hu, M. S., et al., Local Fractional Fourier Series with Application to wave Equation in Fractal Vibrating String, Abstract and Applied Analysis, 2012 (2012), Article ID 567401
    • (2012) Abstract and Applied Analysis , vol.2012
    • Hu, M.S.1
  • 39
    • 84857467321 scopus 로고    scopus 로고
    • Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral
    • Zhong, W. P., et al., Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral, Advanced Materials Research, 461 (2012), pp. 306-310
    • (2012) Advanced Materials Research , vol.461 , pp. 306-310
    • Zhong, W.P.1
  • 40
    • 84869494625 scopus 로고    scopus 로고
    • Asymptotic Methods for Solitary Solutions and Compactions
    • Article ID 916793
    • He, J.-H., Asymptotic Methods for Solitary Solutions and Compactions, Abstract and Applied Analysis, 2012 (2012), Article ID 916793
    • (2012) Abstract and Applied Analysis , vol.2012
    • He, J.-H.1


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