Analytical Solution of Generalized Space-Time Fractional Cable Equation

Ram K. Saxena, Zivorad Tomovski and Trifce Sandev
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Ram K. Saxena: Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, India
Zivorad Tomovski: Department of Mathematics, University of Rijeka, Radmile Matejcic 2, 51000 Rijeka, Croatia
Trifce Sandev: Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia

Mathematics, 2015, vol. 3, issue 2, 1-18

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.

Keywords: fractional cable equation; Mittag-Lef?er functions; H-function; moments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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