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Volumn 14, Issue 9-10, 2008, Pages 1267-1290

Time-fractional diffusion of distributed order

Author keywords

Anomalous diffusion; Fourier transform; Fractional derivatives; Laplace transform; Mittag Leffler function

Indexed keywords

DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS; SEMICONDUCTOR DOPING; SOLUTIONS;

EID: 52349083860     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546307087452     Document Type: Conference Paper
Times cited : (195)

References (57)
  • 1
    • 0035538580 scopus 로고    scopus 로고
    • Spectral analysis of fractional kinetic equations with random data
    • Anh, V.V. and Leonenko, N.N., 2001, " Spectral analysis of fractional kinetic equations with random data, " Journal of Statistical Physics 104 (5 / 6). 1349-1387.
    • (2001) Journal of Statistical Physics , vol.104 , Issue.5 , pp. 1349-1387
    • Anh, V.V.1    Leonenko, N.N.2
  • 3
    • 0001342751 scopus 로고    scopus 로고
    • On the existence of the order domain and the solution of distributed order equations, Part i
    • Bagley, R.L. and Torvik, P.J., 2000 a, " On the existence of the order domain and the solution of distributed order equations, Part I, " International Journal ofApplied Mathematics 2, 865-882.
    • (2000) International Journal OfApplied Mathematics , vol.2 , pp. 865-882
    • Bagley, R.L.1    Torvik, P.J.2
  • 4
    • 0001342751 scopus 로고    scopus 로고
    • On the existence of the order domain and the solution of distributed order equations, Part II
    • Bagley, R.L. and Torvik, P.J., 2000 b, " On the existence of the order domain and the solution of distributed order equations, Part II, " International Journal of Applied Mathematics 2, 965-987.
    • (2000) International Journal of Applied Mathematics , vol.2 , pp. 965-987
    • Bagley, R.L.1    Torvik, P.J.2
  • 5
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent, Part II
    • Caputo, M., 1967, " Linear models of dissipation whose Q is almost frequency independent, Part II, " Geophysical Journal of the Royal Astronomical Society 13, 529-539.
    • (1967) Geophysical Journal of the Royal Astronomical Society , vol.13 , pp. 529-539
    • Caputo, M.1
  • 7
    • 51249169579 scopus 로고
    • Mean fractional-order derivatives differential equations and filters," Annali della Universit di Ferrara (Sezione VII
    • Caputo, M., 1995, " Mean fractional-order derivatives differential equations and filters," Annali della Universit di Ferrara (Sezione VII, Scienze Mathematiche) 41, 73-84.
    • (1995) Scienze Mathematiche , vol.41 , pp. 73-84
    • Caputo, M.1
  • 8
    • 0000227056 scopus 로고    scopus 로고
    • Distributed order differential equations modelling dielectric induction and diffusion
    • Caputo, M., 2001, " Distributed order differential equations modelling dielectric induction and diffusion, " Fractional Calculus and Applied Analysis 4 (4). 421-442.
    • (2001) Fractional Calculus and Applied Analysis , vol.4 , Issue.4 , pp. 421-442
    • Caputo, M.1
  • 10
    • 41349088572 scopus 로고    scopus 로고
    • Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations
    • Chechkin, A.V., Gorenflo, R., and Sokolov, I.M., 2002, " Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations, " Physical Review E 66, 046129 / 1-6.
    • (2002) Physical Review e , vol.66 , pp. 1-6
    • Chechkin, A.V.1    Gorenflo, R.2    Sokolov, I.M.3
  • 12
    • 0041361963 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equation for ultraslow kinetics
    • Chechkin, A.V., Klafter, J., and Sokolov, I.M., 2003 b, " Fractional Fokker-Planck equation for ultraslow kinetics, " Europhysics Letters 63, 326-332.
    • (2003) Europhysics Letters , vol.63 , pp. 326-332
    • Chechkin, A.V.1    Klafter, J.2    Sokolov, I.M.3
  • 13
    • 0012570827 scopus 로고    scopus 로고
    • Numerical solution methods for distributed order differential equations
    • Diethelm, K. and Ford, N.J., 2001, " Numerical solution methods for distributed order differential equations, " Fractional Calculus and Applied Analysis 4, 531-542.
    • (2001) Fractional Calculus and Applied Analysis , vol.4 , pp. 531-542
    • Diethelm, K.1    Ford, N.J.2
  • 14
    • 33748663764 scopus 로고    scopus 로고
    • Numerical solution of linear multi-term initial value problems of fractional order
    • Diethelm, K. and Luchko, Y., 2004, " Numerical solution of linear multi-term initial value problems of fractional order, " Computational Methods of Numerical Analysis 6, 243-263.
    • (2004) Computational Methods of Numerical Analysis , vol.6 , pp. 243-263
    • Diethelm, K.1    Luchko, Y.2
  • 26
    • 57249098754 scopus 로고    scopus 로고
    • Multi-dimensional solutions of time-fractional diffusion-wave equations
    • Hanyga, A., 2002, " Multi-dimensional solutions of time-fractional diffusion-wave equations, " Proceedings of the Royal Society A 458, 933-957.
    • (2002) Proceedings of the Royal Society A , vol.458 , pp. 933-957
    • Hanyga, A.1
  • 27
    • 0141892685 scopus 로고    scopus 로고
    • Fractional-order system identification based on continuous order-distributions
    • Hartley, T.T. and Lorenzo, C.F., 2003, " Fractional-order system identification based on continuous order-distributions, " Signal Processing 83, 2287-2300.
    • (2003) Signal Processing , vol.83 , pp. 2287-2300
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 30
    • 0000332009 scopus 로고
    • Fractional-order diffusion
    • Kochubei, A.N., 1990, " Fractional-order diffusion, " Differential Equations 26, 485-492.
    • (1990) Differential Equations , vol.26 , pp. 485-492
    • Kochubei, A.N.1
  • 31
    • 33646371459 scopus 로고    scopus 로고
    • Solution of a modified fractional diffusion equation
    • Langlands, T.A.M., 2006, " Solution of a modified fractional diffusion equation, " Physica A 367, 136-144.
    • (2006) Physica A , vol.367 , pp. 136-144
    • Langlands, T.A.M.1
  • 32
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • Lorenzo, C.F. and Hartley, T.T., 2002, " Variable order and distributed order fractional operators, " Nonlinear Dynamics 29, 57-98.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 35
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional diffusion-wave phenomena," Chaos
    • Mainardi, F., 1996, " Fractional relaxation-oscillation and fractional diffusion-wave phenomena," Chaos, Solitons and Fractals 7, 1461-1477.
    • (1996) Solitons and Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 36
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • Fractals and Fractional Calculus in Continuum Mechanics A. Carpinteri and F. Mainardi, eds., Springer Verlag, Berlin, pp.
    • Mainardi, F., 1997, " Fractional calculus: Some basic problems in continuum and statistical mechanics," in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., CISM Courses and Lecture Notes, Vol. 378, Springer Verlag, Berlin, pp. 291-348. http://www.fracalmo.org
    • (1997) CISM Courses and Lecture Notes , pp. 291-348
    • Mainardi, F.1
  • 38
    • 0037457788 scopus 로고    scopus 로고
    • The Wright functions as solutions of the time-fractional diffusion equations
    • Mainardi, F. and Pagnini, G., 2003, " The Wright functions as solutions of the time-fractional diffusion equations, " Applied Mathematics and Computation 141 (1). 51-62.
    • (2003) Applied Mathematics and Computation , vol.141 , Issue.1 , pp. 51-62
    • Mainardi, F.1    Pagnini, G.2
  • 39
    • 34547102267 scopus 로고    scopus 로고
    • The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
    • Mainardi, F. and Pagnini, G., 2007, " The role of the Fox-Wright functions in fractional sub-diffusion of distributed order, " Journal of Computational andAppliedMathematics, 207 (2). 245-257.
    • (2007) Journal of Computational AndAppliedMathematics , vol.207 , Issue.2 , pp. 245-257
    • Mainardi, F.1    Pagnini, G.2
  • 40
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi, F., Luchko, Y., and Pagnini, G., 2001, " The fundamental solution of the space-time fractional diffusion equation, " Fractional Calculus andAppliedAnalysis 4, 153-192. http://www.fracalmo.org
    • (2001) Fractional Calculus AndAppliedAnalysis , vol.4 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 42
    • 34247367101 scopus 로고    scopus 로고
    • Some aspects of fractional diffusion equations of single and distributed order
    • Mainardi, F., Pagnini, G., and Gorenflo, R., 2006 b, " Some aspects of fractional diffusion equations of single and distributed order, " Applied Mathematics and Computation, 187 (1). 295-305.
    • (2006) Applied Mathematics and Computation , vol.187 , Issue.1 , pp. 295-305
    • Mainardi, F.1    Pagnini, G.2    Gorenflo, R.3
  • 44
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler, R. and Klafter, J., 2000, " The random walk's guide to anomalous diffusion: A fractional dynamics approach, " Physics Reports 339, 1-77.
    • (2000) Physics Reports , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 45
    • 43949160695 scopus 로고
    • Fractional model equation for anomalous diffusion
    • Metzler, R., Glckle, W.G., and Nonnenmacher, T.F., 1994, " Fractional model equation for anomalous diffusion, " Physica A 211, 13-24.
    • (1994) Physica A , vol.211 , pp. 13-24
    • Metzler, R.1    Glckle, W.G.2    Nonnenmacher, T.F.3
  • 47
    • 4544299160 scopus 로고    scopus 로고
    • Distributed order fractional subdiffusion
    • Naber, M., 2004, " Distributed order fractional subdiffusion, " Fractals 12 (1). 23-32.
    • (2004) Fractals , vol.12 , Issue.1 , pp. 23-32
    • Naber, M.1
  • 49
    • 0000599032 scopus 로고    scopus 로고
    • Fractional kinetic equations: Solutions and applications
    • 764
    • Saichev, A. and Zaslavsky, G.M., 1997, " Fractional kinetic equations: Solutions and applications, " Chaos 7, 753-764.
    • (1997) Chaos , vol.7
    • Saichev, A.1    Zaslavsky, G.M.2
  • 52
    • 31144434675 scopus 로고    scopus 로고
    • From diffusion to anomalous diffusion: A century after Einstein's Brownian motion
    • Sokolov, I.M. and Klafter, J., 2005, " From diffusion to anomalous diffusion: A century after Einstein's Brownian motion, " Chaos 15, 026103-026109.
    • (2005) Chaos , vol.15 , pp. 026103-026109
    • Sokolov, I.M.1    Klafter, J.2
  • 54
    • 32044453310 scopus 로고    scopus 로고
    • Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations: Part one
    • Umarov, S. and Gorenflo, R., 2005, " Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations: Part one, " Zeitschrift fr Analysis und ihre Anwendungen 24 (3). 449-466.
    • (2005) Zeitschrift Fr Analysis und Ihre Anwendungen , vol.24 , Issue.3 , pp. 449-466
    • Umarov, S.1    Gorenflo, R.2
  • 56
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics and anomalous transport
    • Zaslavsky, G.M., 2002, " Chaos, fractional kinetics and anomalous transport, " Physics Reports 371, 461-580.
    • (2002) Physics Reports , vol.371 , pp. 461-580
    • Zaslavsky, G.M.1


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