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Volumn 3, Issue 2, 2010, Pages 209-220

Solving partial fractional differential equations using the ℒ a-transform

Author keywords

fractional derivatives; fractional diffusion equation; fractional disturbance equation; The A transform; Wright functions

Indexed keywords


EID: 84555160808     PISSN: 17935571     EISSN: 17937183     Source Type: Journal    
DOI: 10.1142/S1793557110000143     Document Type: Article
Times cited : (19)

References (32)
  • 1
    • 78651589438 scopus 로고    scopus 로고
    • Complex inversion formula for Stieltjes and Widder transforms with applications
    • A. Aghili and A. Ansari, Complex inversion formula for Stieltjes and Widder transforms with applications, J. Contemp. Math. Sciences 2 (2008) 761-770.
    • (2008) J. Contemp. Math. Sciences , vol.2 , pp. 761-770
    • Aghili, A.1    Ansari, A.2
  • 3
    • 34247185764 scopus 로고    scopus 로고
    • Identities for the E2;1-transform and their applications
    • D. Brown, N. Dernek and O. Yurekli, Identities for the E2;1-transform and their applications, Appl. Math. Comput. 187 (2007) 1557-1566.
    • (2007) Appl. Math. Comput. , vol.187 , pp. 1557-1566
    • Brown, D.1    Dernek, N.2    Yurekli, O.3
  • 4
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent II
    • M. Caputo, Linear models of dissipation whose Q is almost frequency independent II, Geophys. J. Roy. Astronom. Soc. 13 (1967) 529-539.
    • (1967) Geophys. J. Roy. Astronom. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 6
    • 0000227056 scopus 로고    scopus 로고
    • Distributed order difierential equations modeling dielectric induction and diffusion
    • M. Caputo, Distributed order difierential equations modeling dielectric induction and diffusion, Fract. Calc. Appl. Anal. 4 (2001) 421-442.
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 421-442
    • Caputo, M.1
  • 9
    • 36149036329 scopus 로고
    • Fractional diffusion equation on fractals: One-dimensional case and asymptotic behaviour
    • M. Giona and H. E. Roman, Fractional diffusion equation on fractals: One-dimensional case and asymptotic behaviour, J. Phys. A: Math. Gen. 25 (1992) 2107-2117.
    • (1992) J. Phys. A: Math. Gen. , vol.25 , pp. 2107-2117
    • Giona, M.1    Roman, H.E.2
  • 10
    • 0000009397 scopus 로고    scopus 로고
    • Analytical properties and applications of the Wright function
    • R. Goreno, Yu. Luchko and F. Mainardi, Analytical properties and applications of the Wright function, Fract. Calc. Appl. Anal. 2 (1999) 383-414.
    • (1999) Fract. Calc. Appl. Anal. , vol.2 , pp. 383-414
    • Goreno, R.1    Luchko, Yu.2    Mainardi, F.3
  • 11
    • 0000103589 scopus 로고    scopus 로고
    • Wright functions as scale-invariant solutions of the diffusion-wave equation
    • R. Goreno, Yu. 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
    • Goreno, R.1    Luchko, Yu.2    Mainardi, F.3
  • 14
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • A. Carpinteri, F. Mainardi (Eds.), SpringerVerlag, Wien and New York,a Reprinted in NEWS 011201. Available at
    • F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien and New York, 1997, 291-348, Reprinted in NEWS 011201. Available at http://www.fracalmo.org.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 15
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solutions for the fractional diffusion-wave equation
    • F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett. 9 (6) (1996) 23-28.
    • (1996) Appl. Math. Lett. , vol.9 , Issue.6 , pp. 23-28
    • Mainardi, F.1
  • 16
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Available at
    • F. Mainardi, Yu. Luchko and G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fractional Calculus and Applied Analysis 4 (2) (2001) 153-192, Available at http://www.fracalmo.org.
    • (2001) Fractional Calculus and Applied Analysis , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko, Yu.2    Pagnini, G.3
  • 17
    • 34547102267 scopus 로고    scopus 로고
    • The role of the Fox-Wright functions in fractional subdiffusion of distributed order
    • F. Mainardi and G. Pagnini, The role of the Fox-Wright functions in fractional subdiffusion of distributed order, J. Comput. Appl. Math. 207 (2007) 245-257.
    • (2007) J. Comput. Appl. Math. , vol.207 , pp. 245-257
    • Mainardi, F.1    Pagnini, G.2
  • 18
    • 0037457788 scopus 로고    scopus 로고
    • The Wright functions as solutions of the time-fractional diffusion equation
    • F. Mainardi and G. Pagnini, The Wright functions as solutions of the time-fractional diffusion equation, J. Comput. Appl. Math. 141 (2003) 51-62.
    • (2003) J. Comput. Appl. Math. , vol.141 , pp. 51-62
    • Mainardi, F.1    Pagnini, G.2
  • 19
    • 34247367101 scopus 로고    scopus 로고
    • Some aspects of fractional diffusion equations of single and distributed order
    • F. Mainardi, G. Pagnini and R. Goreno, Some aspects of fractional diffusion equations of single and distributed order, Comput. Appl. Math. 187 (2007) 295-305.
    • (2007) Comput. Appl. Math. , vol.187 , pp. 295-305
    • Mainardi, F.1    Pagnini, G.2    Goreno, R.3
  • 20
    • 4544299160 scopus 로고    scopus 로고
    • Distributed order fractional subdiffusion
    • M. Naber, Distributed order fractional subdiffusion, Fractals 12 (2004) 23-32.
    • (2004) Fractals , vol.12 , pp. 23-32
    • Naber, M.1
  • 22
    • 0000117917 scopus 로고
    • Fractional diffusion equation on fractals: Threedimensional case and scattering function
    • H. E. Roman and M. Giona, Fractional diffusion equation on fractals: Threedimensional case and scattering function, J. Phys. A: Math. Gen. 25 (1992) 2107-2117.
    • (1992) J. Phys. A: Math. Gen. , vol.25 , pp. 2107-2117
    • Roman, H.E.1    Giona, M.2
  • 24
    • 0019586367 scopus 로고
    • On the evolution of disturbances at an inviscid interface
    • P. N. Shankar, On the evolution of disturbances at an inviscid interface, J. Fluid Mech. 108 (1981) 159-170.
    • (1981) J. Fluid Mech. , vol.108 , pp. 159-170
    • Shankar, P.N.1
  • 25
    • 32044453310 scopus 로고    scopus 로고
    • Cauchy and nonlocal multi-point problems for distributed order pseudo-difierential equations: Part one
    • S. Umarov and R. Goreno, Cauchy and nonlocal multi-point problems for distributed order pseudo-difierential equations: Part one, Z. Anal. Anwendungen 24 (2005) 449-466.
    • (2005) Z. Anal. Anwendungen , vol.24 , pp. 449-466
    • Umarov, S.1    Goreno, R.2
  • 26
    • 84963017682 scopus 로고
    • On the coečients of power series having exponential singularities
    • E. M. Wright, On the coečients of power series having exponential singularities, J. London Math. Soc. 8 (1933) 71-79.
    • (1933) J. London Math. Soc. , vol.8 , pp. 71-79
    • Wright, E.M.1
  • 27
    • 84963107692 scopus 로고
    • The asymptotic expansion of the generalized Bessel function
    • E. M. Wright, The asymptotic expansion of the generalized Bessel function, Proc. London Math. Soc. (Ser.II) 38 (1935) 257-270.
    • (1935) Proc. London Math. Soc. (Ser.II , vol.38 , pp. 257-270
    • Wright, E.M.1
  • 28
    • 84963044459 scopus 로고
    • The asymptotic expansion of the generalized hypergeometric function
    • E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc. 10 (1935) 287-293.
    • (1935) J. London Math. Soc. , vol.10 , pp. 287-293
    • Wright, E.M.1
  • 29
    • 0012719785 scopus 로고
    • The generalized Bessel function of order greater than one
    • E. M. Wright, The generalized Bessel function of order greater than one, Quart. J. Math. Oxford Ser. 11 (1940) 36-48.
    • (1940) Quart. J. Math. Oxford Ser. , vol.11 , pp. 36-48
    • Wright, E.M.1
  • 31
    • 0040441830 scopus 로고    scopus 로고
    • 2-transforms and their applications
    • 2-transforms and their applications, Appl. Math. Comput. 99 (1999) 141-151.
    • (1999) Appl. Math. Comput. , vol.99 , pp. 141-151
    • Yurekli, O.1
  • 32
    • 0039541703 scopus 로고
    • A Parseval-Goldstein type theorem on the Widder potential transform and its applications
    • O. Yurekli and I. Sadek, A Parseval-Goldstein type theorem on the Widder potential transform and its applications, Int. J. Math. Math. Sci. 14 (1991) 517-524.
    • (1991) Int. J. Math. Math. Sci. , vol.14 , pp. 517-524
    • Yurekli, O.1    Sadek, I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.