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Mathematics 2015, 3(2), 153-170; doi:10.3390/math3020153

Analytical Solution of Generalized Space-Time Fractional Cable Equation

1
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, India
2
Department of Mathematics, University of Rijeka, Radmile Matejcic 2, 51000 Rijeka, Croatia
3
Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje, Macedonia
4
Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia
5
Max Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden, Germany
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 7 March 2015 / Accepted: 2 April 2015 / Published: 9 April 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
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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. View Full-Text
Keywords: fractional cable equation; Mittag-Leffler functions; H-function; moments fractional cable equation; Mittag-Leffler functions; H-function; moments
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Saxena, R.K.; Tomovski, Z.; Sandev, T. Analytical Solution of Generalized Space-Time Fractional Cable Equation. Mathematics 2015, 3, 153-170.

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