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Analytical Solution of Generalized Space-Time Fractional Cable Equation

Author

Listed:
  • Ram K. Saxena

    (Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, India
    These authors contributed equally to this work.)

  • Zivorad Tomovski

    (Department of Mathematics, University of Rijeka, Radmile Matejcic 2, 51000 Rijeka, Croatia
    Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje, Macedonia)

  • Trifce Sandev

    (Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia
    Max Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden, Germany
    These authors contributed equally to this work.)

Abstract

In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.

Suggested Citation

  • Ram K. Saxena & Zivorad Tomovski & Trifce Sandev, 2015. "Analytical Solution of Generalized Space-Time Fractional Cable Equation," Mathematics, MDPI, vol. 3(2), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:2:p:153-170:d:47957
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    References listed on IDEAS

    as
    1. Sandev, Trifce & Tomovski, Živorad & Dubbeldam, Johan L.A., 2011. "Generalized Langevin equation with a three parameter Mittag-Leffler noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3627-3636.
    2. Tomovski, Živorad & Sandev, Trifce & Metzler, Ralf & Dubbeldam, Johan, 2012. "Generalized space–time fractional diffusion equation with composite fractional time derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2527-2542.
    3. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    4. Yasuhiro Fujita, 1993. "A generalization of the results of Pillai," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 361-365, June.
    5. Hilfer, R., 1995. "An extension of the dynamical foundation for the statistical equilibrium concept," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 89-96.
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