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Volumn 14, Issue 2, 2013, Pages 127-133

Approximate solutions for diffusion equations on cantor space-time

Author keywords

Adomian decomposition method; Approximate solutions; Cantor sets; Diffusion equations; Local fractional operators

Indexed keywords


EID: 84878993985     PISSN: 14549069     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (110)

References (63)
  • 1
    • 0000355573 scopus 로고    scopus 로고
    • Time symmetry breaking, duality and cantorian space-time
    • 505-518
    • M.S. EL NASCHIE, Time symmetry breaking, duality and Cantorian space-time, Chaos, Solitons & Fractals, 7, pp. 499-503, 505-518, 1996.
    • (1996) Chaos, Solitons & Fractals , vol.7 , pp. 499-503
    • El Naschie, M.S.1
  • 2
    • 0038086924 scopus 로고
    • Scale relativity, fractal space-time and quantum mechanics
    • edited by M. S. El Naschie, O. Rossler and I. Prigogine, Elsevier, Oxford
    • L. NOTTALE, Scale relativity, fractal space-time and quantum mechanics, in Quantum Mechanics, Diffusion and Chaotic Fractals, edited by M. S. El Naschie, O. Rossler and I. Prigogine, Elsevier, Oxford, 1995, pp. 51-78.
    • (1995) Quantum Mechanics, Diffusion and Chaotic Fractals , pp. 51-78
    • Nottale, L.1
  • 5
    • 85081776055 scopus 로고    scopus 로고
    • Heisenberg uncertainty principles in local fractional fourier analysis
    • accepted
    • X.J. YANG, D. BALEANU, J.A.T. MACHADO, Heisenberg uncertainty principles in local fractional Fourier analysis, Frac. Calc. Appl. Anal., accepted, 2012.
    • (2012) Frac. Calc. Appl. Anal.
    • Yang, X.J.1    Baleanu, D.2    Machado, J.A.T.3
  • 7
    • 84555221318 scopus 로고    scopus 로고
    • Local fractional integral transforms
    • X.J. YANG, Local fractional integral transforms, Progress in Nonlinear Science, 4, pp.1-225, 2011.
    • (2011) Progress in Nonlinear Science , vol.4 , pp. 1-225
    • Yang, X.J.1
  • 8
    • 84555190014 scopus 로고    scopus 로고
    • On the convolution equation related to the diamond klein-gordon operator
    • A. LIANGPROM, K. NONLAOPOU, On the convolution equation related to the diamond Klein-Gordon operator, Abstr. Appl. Anal., 908491, 2011.
    • (2011) Abstr. Appl. Anal. , pp. 908491
    • Liangprom, A.1    Nonlaopou, K.2
  • 11
    • 84979765962 scopus 로고
    • Under diffusion
    • A. FICK, Under diffusion, Ann. Phys. (Leipzig), 170, pp. 59-86, 1855.
    • (1855) Ann. Phys. (Leipzig) , vol.170 , pp. 59-86
    • Fick, A.1
  • 12
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. METZLER, J. KLAFTER, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep., 339, pp. 1-77, 2000.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 13
    • 78049490565 scopus 로고    scopus 로고
    • The general time fractional wave equation for a vibrating string
    • T. SANDEY, Z. TOMOVSKI, The general time fractional wave equation for a vibrating string, J. Phys. A, 43, 5, 055204, 2010.
    • (2010) J. Phys. A , vol.43 , Issue.5 , pp. 055204
    • Sandey, T.1    Tomovski, Z.2
  • 14
    • 70349213975 scopus 로고    scopus 로고
    • Generalized wave equation in nonlocal elasticity
    • T. M. ATANACKOVIC, B. STANKOVIC, Generalized wave equation in nonlocal elasticity, Acta Mech., 208, 1-2, pp.1-10, 2009.
    • (2009) Acta Mech. , vol.208 , Issue.1-2 , pp. 1-10
    • Atanackovic, T.M.1    Stankovic, B.2
  • 15
    • 0009481303 scopus 로고
    • The fractional diffusion equation
    • W. WYSS, The fractional diffusion equation, J. Math. Phys., 27, pp. 2782-2785, 1986.
    • (1986) J. Math. Phys. , vol.27 , pp. 2782-2785
    • Wyss, W.1
  • 16
    • 0000361678 scopus 로고    scopus 로고
    • Random walk models for space fractional diffusion processes
    • R. GORENFLO, F. MAINARDI, Random Walk Models for Space Fractional Diffusion Processes, Frac. Calc. Appl. Anal., 1, pp.167-191, 1998.
    • (1998) Frac. Calc. Appl. Anal. , vol.1 , pp. 167-191
    • Gorenflo, R.1    Mainardi, F.2
  • 17
    • 0001407424 scopus 로고    scopus 로고
    • The fundanental solution of the space-time fractional diffusion equation
    • F. MAINARDI, YU. LUCHKO, G. PAGNINI, The fundanental solution of the space-time fractional diffusion equation, Frac. Calc. Appl. Anal., 4, 2, pp.153-192, 2001.
    • (2001) Frac. Calc. Appl. Anal. , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko, Yu.2    Pagnini, G.3
  • 19
    • 52549095901 scopus 로고    scopus 로고
    • Fractional control of heat diffusion systems
    • I.S. JESUS, J.A.T. MACHADO, Fractional control of heat diffusion systems, Nonlin. Dyn., 54, 3, pp. 263-282, 2008.
    • (2008) Nonlin. Dyn. , vol.54 , Issue.3 , pp. 263-282
    • Jesus, I.S.1    Machado, J.A.T.2
  • 20
    • 1942542248 scopus 로고    scopus 로고
    • Cauchy problem for fractional diffusion equations
    • DOI 10.1016/j.jde.2003.12.002
    • S.D. EIDELMAN, A.N. KOCHUBEI, Cauchy problem for fractional diffusion equations, J. Diff. Equ., 199, pp. 211-255, 2004. (Pubitemid 38516155)
    • (2004) Journal of Differential Equations , vol.199 , Issue.2 , pp. 211-255
    • Eidelman, S.D.1    Kochubei, A.N.2
  • 22
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solutions for the fractional diffusion-wave equation
    • DOI 10.1016/0893-9659(96)00089-4, PII S0893965996000894
    • F. MAINARDI, The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett., 9, 6, pp. 23-28, 1996. (Pubitemid 126365654)
    • (1996) Applied Mathematics Letters , vol.9 , Issue.6 , pp. 23-28
    • Mainardi, F.1
  • 23
    • 0036828936 scopus 로고    scopus 로고
    • Space- and time-fractional diffusion and wave equations, fractional fokker-planck equations, and physical motivation
    • R. METZLER, T.F. NONNENMACHER, Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation, Chem. Phys. 284, pp. 67-90, 2002.
    • (2002) Chem. Phys. , vol.284 , pp. 67-90
    • Metzler, R.1    Nonnenmacher, T.F.2
  • 24
    • 0030531939 scopus 로고    scopus 로고
    • Fractional-order diffusion-wave equation
    • A.M.A. El-SAYED, Fractional-order diffusion-wave equation, Int. J. Theor. Phys., 35, 2, pp. 311-322, 1996.
    • (1996) Int. J. Theor. Phys. , vol.35 , Issue.2 , pp. 311-322
    • El-Sayed, A.M.A.1
  • 25
    • 8644239830 scopus 로고    scopus 로고
    • Fractional diffusion equations with internal degrees of freedom
    • L VAZQUEZ, Fractional diffusion equations with internal degrees of freedom, J. Comput. Math., 21, 4, pp. 491-494, 2003.
    • (2003) J. Comput. Math. , vol.21 , Issue.4 , pp. 491-494
    • Vazquez, L.1
  • 30
    • 84872148874 scopus 로고    scopus 로고
    • Local fractional fourier series with application to wave equation in fractal vibrating string
    • M.S. HU, R.P. AGARWAL, X.J. YANG, Local fractional Fourier series with application to wave equation in fractal vibrating string, Abstr. Appl. Anal., 567401, 2013.
    • (2013) Abstr. Appl. Anal. , pp. 567401
    • Hu, M.S.1    Agarwal, R.P.2    Yang, X.J.3
  • 31
    • 84879001387 scopus 로고    scopus 로고
    • A new adomian decomposition procedure scheme for solving local fractional volterra integral equation
    • X.J. YANG, Y.D. ZHANG, A new Adomian decomposition procedure scheme for solving local fractional Volterra integral equation, Adv. Information Technology and Manag., 1, 4, pp.158-161, 2012.
    • (2012) Adv. Information Technology and Manag. , vol.1 , Issue.4 , pp. 158-161
    • Yang, X.J.1    Zhang, Y.D.2
  • 33
    • 65049090377 scopus 로고    scopus 로고
    • Numerical algorithm based on adomian decomposition for fractional differential equations
    • C. LI, Y. WANG, Numerical algorithm based on Adomian decomposition for fractional differential equations, Comput. Math. Appl., 57, pp. 1672-1681, 2009.
    • (2009) Comput. Math. Appl. , vol.57 , pp. 1672-1681
    • Li, C.1    Wang, Y.2
  • 34
    • 79953679592 scopus 로고    scopus 로고
    • Approximate solutions to fractional subdiffusion equations
    • J. HRISTOV, Approximate solutions to fractional subdiffusion equations, The Eur. Phys. J. Spec. Topics, 193, pp. 229-243, 2011.
    • (2011) The Eur. Phys. J. Spec. Topics , vol.193 , pp. 229-243
    • Hristov, J.1
  • 35
    • 84874054174 scopus 로고    scopus 로고
    • A review of the adomian decomposition method and its applications to fractional differential equations
    • J.S. DUAN, R. RACH, D. BALEANU, A.M. WAZWAZ, A review of the Adomian decomposition method and its applications to fractional differential equations, Commun. Frac. Calc., 3, pp.73-99, 2012.
    • (2012) Commun. Frac. Calc. , vol.3 , pp. 73-99
    • Duan, J.S.1    Rach, R.2    Baleanu, D.3    Wazwaz, A.M.4
  • 36
    • 31744438550 scopus 로고    scopus 로고
    • A second-order accurate numerical approximation for the fractional diffusion equation
    • DOI 10.1016/j.jcp.2005.08.008, PII S0021999105003773
    • C. TADJERAN, M.M. MEERSCHAERT, H.P. SCHEFFLER, A second-order accurate numerical approximation for the fractional diffusion equation, J. Comput. Phys., 213, pp. 205-13, 2006. (Pubitemid 43174872)
    • (2006) Journal of Computational Physics , vol.213 , Issue.1 , pp. 205-213
    • Tadjeran, C.1    Meerschaert, M.M.2    Scheffler, H.-P.3
  • 37
    • 33749512364 scopus 로고    scopus 로고
    • Approximate solutions for boundary value problems of time-fractional wave equation
    • DOI 10.1016/j.amc.2006.02.004, PII S0096300306001573
    • Z.M. ODIBAT, S. MOMANI, Approximate solutions for boundary value problems of time-fractional wave equation, Appl. Math. Comput., 181, pp.767-774, 2006. (Pubitemid 44528059)
    • (2006) Applied Mathematics and Computation , vol.181 , Issue.1 , pp. 767-774
    • Odibat, Z.M.1    Momani, S.2
  • 38
    • 58849156443 scopus 로고    scopus 로고
    • Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition
    • X.C. LI, M.Y. XU, X.Y. JIANG, Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition, Appl. Math. Comput., 208, pp. 434-439, 2009.
    • (2009) Appl. Math. Comput. , vol.208 , pp. 434-439
    • Li, X.C.1    Xu, M.Y.2    Jiang, X.Y.3
  • 39
    • 33747605785 scopus 로고    scopus 로고
    • Hybrid symbolic and numerical simulation studies of time-fractional order wave-diffusion systems
    • DOI 10.1080/00207170600726493, PII R25P69013J741W71
    • J. LIANG, Y.Q. CHEN, Hybrid symbolic and numerical simulation studies of time-fractional order wave-diffusion systems, Int. J. Contr., 79, pp.1462-1470, 2006. (Pubitemid 44267818)
    • (2006) International Journal of Control , vol.79 , Issue.11 , pp. 1462-1470
    • Liang, J.1    Chen, Y.Q.2
  • 40
    • 84867978055 scopus 로고    scopus 로고
    • Implicit difference approximation for the time fractional diffusion equation
    • Extra Edition
    • P. ZHYANG, F. LIU, Implicit difference approximation for the time fractional diffusion equation, J. Appl. Math. Computing, 22, 3, pp.87-99, 2006. (Pubitemid 44695544)
    • (2006) Journal of Applied Mathematics and Computing , vol.22 , Issue.3 , pp. 87-99
    • Zhuang, P.1    Liu, F.2
  • 41
    • 34249011674 scopus 로고    scopus 로고
    • Multi-dimensional solutions of space-time-fractional diffusion equations
    • A. HANYGA, Multi-dimensional solutions of space-time-fractional diffusion equations, Proc. R. Soc. Lond. A, 458, pp. 429-450, 2002.
    • (2002) Proc. R. Soc. Lond. A , vol.458 , pp. 429-450
    • Hanyga, A.1
  • 42
    • 67149103784 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. I. Volterra-type equation
    • T.M. ATANACKOVIC, S. PILIPOVIC, D. ZORICA, Time distributed-order diffusion-wave equation. I. Volterra-type equation, Proc. R. Soc. A, 465, pp.1869-1891, 2009.
    • (2009) Proc. R. Soc. A , vol.465 , pp. 1869-1891
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 43
    • 67149125441 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. II. Applications of laplace and fourier transformations
    • T.M. ATANACKOVIC, S. PILIPOVIC, D. ZORICA, Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations, Proc. R. Soc. A, 465, pp. 1893-1917, 2009.
    • (2009) Proc. R. Soc. A , vol.465 , pp. 1893-1917
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 44
    • 0025548782 scopus 로고
    • A review of the decomposition method and some recent results for nonlinear equation
    • G. ADOMIAN, A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Model., 13 (7), pp.17-43, 1990.
    • (1990) Math. Comput. Model. , vol.13 , Issue.7 , pp. 17-43
    • Adomian, G.1
  • 46
    • 33749534281 scopus 로고    scopus 로고
    • The decomposition method for initial value problems
    • DOI 10.1016/j.amc.2006.01.025, PII S0096300306000919
    • D. LESNIC, The decomposition method for initial value problems, Appl. Math. Comput., 181, pp. 206-213, 2006. (Pubitemid 44528012)
    • (2006) Applied Mathematics and Computation , vol.181 , Issue.1 , pp. 206-213
    • Lesnic, D.1
  • 47
    • 0034276401 scopus 로고    scopus 로고
    • Approximate solutions to boundary value problems of higher order by the modified decomposition method
    • A.M. WAZWAZ, Approximate solutions to boundary value problems of higher order by the modified decomposition method, Comput. Math. Appl., 40, pp. 679-691, 2000.
    • (2000) Comput. Math. Appl. , vol.40 , pp. 679-691
    • Wazwaz, A.M.1
  • 48
    • 33744989624 scopus 로고    scopus 로고
    • A laplace decomposition algorithm applied to a class of nonlinear differential equations
    • S.A. KHURI, A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1, 4, pp.141-155, 2001.
    • (2001) J. Appl. Math. , vol.1 , Issue.4 , pp. 141-155
    • Khuri, S.A.1
  • 49
    • 77950456001 scopus 로고    scopus 로고
    • An effective modification of the laplace decomposition method for nonlinear equations
    • Y. KHAN, An effective modification of the Laplace decomposition method for nonlinear equations, Int. J. Nonlin. Sci. Num. Simul., 10, pp.1373-1376, 2009.
    • (2009) Int. J. Nonlin. Sci. Num. Simul. , vol.10 , pp. 1373-1376
    • Khan, Y.1
  • 51
    • 84860388823 scopus 로고    scopus 로고
    • A short remark on fractional variational iteration method
    • J.H. HE, A short remark on fractional variational iteration method, Phys. Lett. A, 375, pp. 3362-3364, 2011.
    • (2011) Phys. Lett. A , vol.375 , pp. 3362-3364
    • He, J.H.1
  • 52
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method - A kind of nonlinear analytical technique: Some examples
    • J.H. HE, Variational iteration method-a kind of nonlinear analytical technique: some examples, Int. J. Non-Linear Mech., 34, pp.708-799, 1999.
    • (1999) Int. J. Non-Linear Mech. , vol.34 , pp. 708-799
    • He, J.H.1
  • 53
    • 80054719561 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving a system of schrödinger- korteweg-de vries equations
    • A.K. GOLMANKHANEH et al., Homotopy perturbation method for solving a system of Schrödinger-Korteweg-de Vries equations, Rom. Rep. Phys., 63, 3, pp. 609-623, 2011.
    • (2011) Rom. Rep. Phys. , vol.63 , Issue.3 , pp. 609-623
    • Golmankhaneh, A.K.1
  • 54
    • 79953886340 scopus 로고    scopus 로고
    • On fractional hamiltonian systems possessing first-class constraints within caputo derivatives
    • D. BALEANU et al., On fractional Hamiltonian systems possessing first-class constraints within Caputo derivatives, Rom. Rep. Phys., 63, 1, pp. 3-8, 2011.
    • (2011) Rom. Rep. Phys. , vol.63 , Issue.1 , pp. 3-8
    • Baleanu, D.1
  • 55
    • 84861715300 scopus 로고    scopus 로고
    • Solutions of the fractional davey-stewartson equations with variational iteration method
    • H. JAFARI et al., Solutions of the fractional Davey-Stewartson equations with variational iteration method, Rom. Rep. Phys., 64, 2, pp. 337-346 (2012).
    • (2012) Rom. Rep. Phys. , vol.64 , Issue.2 , pp. 337-346
    • Jafari, H.1
  • 56
    • 84869470751 scopus 로고    scopus 로고
    • Fractional-order two-electric pendulum
    • D. BALEANU et al., Fractional-order two-electric pendulum, Rom. Rep. Phys., 64, 4, 907-914, 2012.
    • (2012) Rom. Rep. Phys. , vol.64 , Issue.4 , pp. 907-914
    • Baleanu, D.1
  • 57
    • 79957633614 scopus 로고    scopus 로고
    • Homotopy perturbation method for the coupled fractional lotka-volterra equations
    • A. KADEM, D. BALEANU, Homotopy perturbation method for the coupled fractional Lotka-Volterra equations, Rom. J. Phys., 56, 3-4, pp. 332-338, 2011.
    • (2011) Rom. J. Phys. , vol.56 , Issue.3-4 , pp. 332-338
    • Kadem, A.1    Baleanu, D.2
  • 58
    • 79959998825 scopus 로고    scopus 로고
    • On fractional coupled whitham-broer-kaup equations
    • A. KADEM, D. BALEANU, On fractional coupled Whitham-Broer-Kaup equations, Rom. J. Phys., 56, 5-6, pp. 629-635, 2011.
    • (2011) Rom. J. Phys. , vol.56 , Issue.5-6 , pp. 629-635
    • Kadem, A.1    Baleanu, D.2
  • 59
    • 84868674070 scopus 로고    scopus 로고
    • On the mittag-leffler stability of Q-fractional nonlinear dynamical systems
    • F. JARAD et al., On the Mittag-Leffler stability of Q-fractional nonlinear dynamical systems, Proc. Romanian Acad. A, 12, 4, pp. 309-314, 2011.
    • (2011) Proc. Romanian Acad. A , vol.12 , Issue.4 , pp. 309-314
    • Jarad, F.1
  • 60
    • 79957644991 scopus 로고    scopus 로고
    • Fractional dimensional harmonic oscillator
    • R. EID, S.I. MUSLIH, D. BALEANU, E. RABEI, Fractional dimensional harmonic oscillator, Rom. J. Phys., 56, 3-), pp. 323-331, 2011.
    • (2011) Rom. J. Phys. , vol.56 , Issue.3 , pp. 323-331
    • Eid, R.1    Muslih, S.I.2    Baleanu, D.3    Rabei, E.4
  • 61
    • 84878990123 scopus 로고    scopus 로고
    • Local fractional variational iteration method and its algorithms
    • X.J. YANG, F.R ZHANG, Local fractional variational iteration method and its algorithms, Adv. Comput. Math. Appl., 1, 3, pp. 139-145, 2012.
    • (2012) Adv. Comput. Math. Appl. , vol.1 , Issue.3 , pp. 139-145
    • Yang, X.J.1    Zhang, F.R.2
  • 63
    • 84869494625 scopus 로고    scopus 로고
    • Asymptotic methods for solitary solutions and compactons
    • J.H. HE, Asymptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012, 916793, 2012.
    • (2012) Abstr. Appl. Anal. , vol.2012 , pp. 916793
    • He, J.H.1


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