메뉴 건너뛰기




Volumn 15, Issue 1, 2012, Pages 1-16

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Author keywords

Fractional calculus; H Fox function; Integral transforms; Mittag Leffler functions

Indexed keywords


EID: 84857684683     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11040-011-9100-8     Document Type: Article
Times cited : (33)

References (31)
  • 1
    • 70350663279 scopus 로고    scopus 로고
    • Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
    • Langlands, T. A. M., Henry, B. I., Wearne, S. L.: Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions. J. Math. Biol. 59, 761-808 (2008).
    • (2008) J. Math. Biol. , vol.59 , pp. 761-808
    • Langlands, T.A.M.1    Henry, B.I.2    Wearne, S.L.3
  • 2
    • 33646371459 scopus 로고    scopus 로고
    • Solution of a modified fractional diffusion equation
    • Langlands, T. A. M.: Solution of a modified fractional diffusion equation. Physica A 367, 136-144 (2006).
    • (2006) Physica A , vol.367 , pp. 136-144
    • Langlands, T.A.M.1
  • 3
    • 77957907967 scopus 로고    scopus 로고
    • The fundamental solutions of the space, space-time Riesz fractional partial differential equations with periodic conditions
    • Zhang, H., Liu, F.: The fundamental solutions of the space, space-time Riesz fractional partial differential equations with periodic conditions. Numer. Math. J. Chinese Univ. (English Ser.) 16, 181-192 (2007).
    • (2007) Numer. Math. J. Chinese Univ. (English Ser.) , vol.16 , pp. 181-192
    • Zhang, H.1    Liu, F.2
  • 4
    • 84857686020 scopus 로고    scopus 로고
    • The problem for fractional diffusion-wave equations on finite interval and laplace transform (in Chinese)
    • Duan, J.-s., Xu, M.-y.: The problem for fractional diffusion-wave equations on finite interval and laplace transform (in Chinese). Appl. Math. J. Chin. Univ. Ser. A 19, 165-171 (2004).
    • (2004) Appl. Math. J. Chin. Univ. Ser. A , vol.19 , pp. 165-171
    • Duan, J.-S.1    Xu, M.-Y.2
  • 5
    • 33745194344 scopus 로고    scopus 로고
    • New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation
    • Yu, R., Zhang, H.: New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation. Chaos, Solitons Fractals 30, 946-955 (2006).
    • (2006) Chaos, Solitons Fractals , vol.30 , pp. 946-955
    • Yu, R.1    Zhang, H.2
  • 6
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi, F., Luchko, Y., Pagnini, G.: The fundamental solution of the space-time fractional diffusion equation. Frac. Calc. Appl. Anal. 4, 153-192 (2001).
    • (2001) Frac. Calc. Appl. Anal. , vol.4 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 8
    • 33845313674 scopus 로고    scopus 로고
    • A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations
    • Mathai, A. M., Saxena, R. K., Haubold, H. J.: A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations. Astrophys. Space Sci. 305, 283-288 (2006).
    • (2006) Astrophys. Space Sci. , vol.305 , pp. 283-288
    • Mathai, A.M.1    Saxena, R.K.2    Haubold, H.J.3
  • 10
    • 0039293981 scopus 로고
    • Sur la Fonction de Mittag-Leffler e Quelques-unes de Ses Généralisations
    • Humbert, P., Agarwal, R. P.: Sur la Fonction de Mittag-Leffler e Quelques-unes de Ses Généralisations. Bull. Sci. Math. 77, 180-185 (1953).
    • (1953) Bull. Sci. Math. , vol.77 , pp. 180-185
    • Humbert, P.1    Agarwal, R.P.2
  • 11
    • 0842337110 scopus 로고
    • a singular integral equation with a generalized Mittag-Leffler function in the kernel
    • Prabhakar, T. R.: a singular integral equation with a generalized Mittag-Leffler function in the kernel. Yokohama Math. J. 19, 7-15 (1971).
    • (1971) Yokohama Math. J. , vol.19 , pp. 7-15
    • Prabhakar, T.R.1
  • 12
  • 15
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guides to anomalous diffusion: a fractional kinetic equation
    • Metzler, R., Klafter, J.: The random walk's guides to anomalous diffusion: a fractional kinetic equation. Phys. Rep. 339, 1-77 (2000).
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 17
    • 78650782808 scopus 로고    scopus 로고
    • Exact solutions of triple-order time-fractional differential equations for anomalous relaxation and diffusion I: the accelerating case
    • Saxena, R. K., Pagnini, G.: Exact solutions of triple-order time-fractional differential equations for anomalous relaxation and diffusion I: the accelerating case. Physica A 390, 602-613 (2011).
    • (2011) Physica A , vol.390 , pp. 602-613
    • Saxena, R.K.1    Pagnini, G.2
  • 18
    • 79953685491 scopus 로고    scopus 로고
    • Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
    • Capelas de Oliveira, E., Mainardi, F., Vaz Jr., J.: Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. Eur. Phys. J. Special Topics 193, 161-171 (2011).
    • (2011) Eur. Phys. J. Special Topics , vol.193 , pp. 161-171
    • Capelas de Oliveira, E.1    Mainardi, F.2    Vaz Jr., J.3
  • 24
    • 50849115153 scopus 로고    scopus 로고
    • Homogeneous fractional embeddings
    • Inizan, P.: Homogeneous fractional embeddings. J. Math. Phys. 49, 082901 (2008).
    • (2008) J. Math. Phys , vol.49 , pp. 82901
    • Inizan, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.