메뉴 건너뛰기




Volumn 47, Issue , 2015, Pages 54-60

Local fractional similarity solution for the diffusion equation defined on Cantor sets

Author keywords

Diffusion equation; Local fractional derivative; Local fractional partial derivative operators; Non differentiability; Similarity solution

Indexed keywords

DIFFUSION; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84939986878     PISSN: 08939659     EISSN: 18735452     Source Type: Journal    
DOI: 10.1016/j.aml.2015.02.024     Document Type: Article
Times cited : (144)

References (24)
  • 2
    • 0004020231 scopus 로고
    • Oxford University Press Oxford, London and New York
    • J. Crank The Mathematics of Diffusion 1975 Oxford University Press Oxford, London and New York
    • (1975) The Mathematics of Diffusion
    • Crank, J.1
  • 3
    • 77956684069 scopus 로고    scopus 로고
    • Theory and Applications of Fractional Differential Equations
    • Elsevier (North-Holland) Science Publishers Amsterdam, London and New York
    • A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematical Studies vol. 204 2006 Elsevier (North-Holland) Science Publishers Amsterdam, London and New York
    • (2006) North-Holland Mathematical Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 7
    • 85012858151 scopus 로고    scopus 로고
    • World Scientific Publishing Company Singapore, New Jersey, London and Hong Kong
    • Y. Zhou Basic Theory of Fractional Differential Equations 2014 World Scientific Publishing Company Singapore, New Jersey, London and Hong Kong
    • (2014) Basic Theory of Fractional Differential Equations
    • Zhou, Y.1
  • 8
    • 84937451593 scopus 로고    scopus 로고
    • Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order, series on complexity
    • World Scientific Publishing Company Singapore, New Jersey, London and Hong Kong
    • D. Baleanu, and O.G. Mustafa Asymptotic integration and stability for ordinary, functional and discrete differential equations of fractional order, series on complexity Nonlinearity and Chaos, vol. 4 2015 World Scientific Publishing Company Singapore, New Jersey, London and Hong Kong
    • (2015) Nonlinearity and Chaos , vol.4
    • Baleanu, D.1    Mustafa, O.G.2
  • 9
    • 0009481303 scopus 로고
    • The fractional diffusion equation
    • W. Wyss The fractional diffusion equation J. Math. Phys. 27 1986 2782 2785
    • (1986) J. Math. Phys. , vol.27 , pp. 2782-2785
    • Wyss, W.1
  • 11
    • 0000103589 scopus 로고    scopus 로고
    • Wright functions as scale-invariant solutions of the diffusion-wave equation
    • R. Gorenflo, Yu.F. Luchko, and F. Mainardi Wright functions as scale-invariant solutions of the diffusion-wave equation J. Comput. Appl. Math. 118 2000 175 191
    • (2000) J. Comput. Appl. Math. , vol.118 , pp. 175-191
    • Gorenflo, R.1    Luchko, Yu.F.2    Mainardi, F.3
  • 12
    • 84897562129 scopus 로고    scopus 로고
    • Similarity solution for fractional diffusion equation
    • J.-S. Duan, A.-P. Guo, and W.-Z. Yun Similarity solution for fractional diffusion equation Abstr. Appl. Anal. 2014 2014 1 5 Article ID 548126
    • (2014) Abstr. Appl. Anal. , vol.2014 , pp. 1-5
    • Duan, J.-S.1    Guo, A.-P.2    Yun, W.-Z.3
  • 14
    • 84925482071 scopus 로고    scopus 로고
    • Fractional calculus for nanoscale flow and heat transfer
    • H.-Y. Liu, J.-H. He, and Z.-B. Li Fractional calculus for nanoscale flow and heat transfer Internat. J. Numer. Method. 24 2014 1227 1250
    • (2014) Internat. J. Numer. Method. , vol.24 , pp. 1227-1250
    • Liu, H.-Y.1    He, J.-H.2    Li, Z.-B.3
  • 15
    • 84939890949 scopus 로고    scopus 로고
    • A tutorial review on fractal spacetime and fractional calculus
    • J.-H. He A tutorial review on fractal spacetime and fractional calculus Internat. J. Theoret. Phys. 53 2014 3698 3718
    • (2014) Internat. J. Theoret. Phys. , vol.53 , pp. 3698-3718
    • He, J.-H.1
  • 16
    • 84881521586 scopus 로고    scopus 로고
    • Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates
    • Y.-J. Hao, H.M. Srivastava, H. Jafari, and X.-J. Yang Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates Adv. Math. Phys. 2013 2013 1 5 Article ID 754248
    • (2013) Adv. Math. Phys. , vol.2013 , pp. 1-5
    • Hao, Y.-J.1    Srivastava, H.M.2    Jafari, H.3    Yang, X.-J.4
  • 17
    • 84935013592 scopus 로고    scopus 로고
    • Local fractional functional method for solving diffusion equations on Cantor sets
    • Y. Cao, W.-G. Ma, and L.-C. Ma Local fractional functional method for solving diffusion equations on Cantor sets Abstr. Appl. Anal. 2014 2014 1 6 Article ID 803693
    • (2014) Abstr. Appl. Anal. , vol.2014 , pp. 1-6
    • Cao, Y.1    Ma, W.-G.2    Ma, L.-C.3
  • 18
    • 84920928257 scopus 로고    scopus 로고
    • Solving initial-boundary value problems for local fractional differential equation by local fractional Fourier series method
    • Y. Zhang Solving initial-boundary value problems for local fractional differential equation by local fractional Fourier series method Abstr. Appl. Anal. 2014 2014 1 5 Article ID 912464
    • (2014) Abstr. Appl. Anal. , vol.2014 , pp. 1-5
    • Zhang, Y.1
  • 19
    • 84884896550 scopus 로고    scopus 로고
    • The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar
    • A.-M. Yang, Y.-Z. Zhang, and Y. Long The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar Thermal Sci. 17 2013 707 713
    • (2013) Thermal Sci. , vol.17 , pp. 707-713
    • Yang, A.-M.1    Zhang, Y.-Z.2    Long, Y.3
  • 20
    • 84881521586 scopus 로고    scopus 로고
    • Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates
    • Y.-J. Hao, H.M. Srivastava, H. Jafari, and X.-J. Yang Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates Adv. Math. Phys. 2013 2013 1 5 Article ID 754248
    • (2013) Adv. Math. Phys. , vol.2013 , pp. 1-5
    • Hao, Y.-J.1    Srivastava, H.M.2    Jafari, H.3    Yang, X.-J.4
  • 21
    • 84890038237 scopus 로고    scopus 로고
    • Application of the local fractional series method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators
    • A.-M. Yang, Z.-S. Chen, H.M. Srivastava, and X.-J. Yang Application of the local fractional series method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators Abstr. Appl. Anal. 2013 2013 1 6 Article ID 259125
    • (2013) Abstr. Appl. Anal. , vol.2013 , pp. 1-6
    • Yang, A.-M.1    Chen, Z.-S.2    Srivastava, H.M.3    Yang, X.-J.4
  • 22
    • 84904652069 scopus 로고    scopus 로고
    • Local fractional Laplace variational iteration method for solving linear partial differential equations with local fractional derivative
    • A.-M. Yang, J. Lie, H.M. Srivastava, G.-N. Xie, and X.-J. Yang Local fractional Laplace variational iteration method for solving linear partial differential equations with local fractional derivative Discrete Dyn. Nat. Soc. 2014 2014 1 8 Article ID 365981
    • (2014) Discrete Dyn. Nat. Soc. , vol.2014 , pp. 1-8
    • Yang, A.-M.1    Lie, J.2    Srivastava, H.M.3    Xie, G.-N.4    Yang, X.-J.5
  • 23
    • 84934914868 scopus 로고    scopus 로고
    • A local fractional integral inequality on fractal space analogous to Anderson's Inequality
    • W. Wie, H.M. Srivastava, Y. Zhang, L. Wang, P. Shen, and J. Zhang A local fractional integral inequality on fractal space analogous to Anderson's Inequality Abstr. Appl. Anal. 2014 2014 1 7 Article ID 797561
    • (2014) Abstr. Appl. Anal. , vol.2014 , pp. 1-7
    • Wie, W.1    Srivastava, H.M.2    Zhang, Y.3    Wang, L.4    Shen, P.5    Zhang, J.6
  • 24
    • 84928410965 scopus 로고    scopus 로고
    • Local fractional variational iteration algorithms for the parabolic Fokker-Planck equation defined on Cantor sets
    • D. Baleanu, H.M. Srivastava, and X.-J. Yang Local fractional variational iteration algorithms for the parabolic Fokker-Planck equation defined on Cantor sets Progr. Fract. Different. Appl. 1 2015 1 11
    • (2015) Progr. Fract. Different. Appl. , vol.1 , pp. 1-11
    • Baleanu, D.1    Srivastava, H.M.2    Yang, X.-J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.