Analytical Solution of Generalized Space-Time Fractional Cable Equation

Analytical Solution of Generalized Space-Time Fractional Cable Equation

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 asympto...

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Main Authors: Ram K. Saxena, Zivorad Tomovski, Trifce Sandev
Format: Article
Language:English
Published: MDPI AG 2015-04-01
Series:Mathematics
Subjects:
fractional cable equation
Mittag-Leffler functions
H-function
moments
Online Access:http://www.mdpi.com/2227-7390/3/2/153
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spelling doaj-57340e8b120642ba80b9e1735835a71c2020-11-25T01:08:03ZengMDPI AGMathematics2227-73902015-04-013215317010.3390/math3020153math3020153Analytical Solution of Generalized Space-Time Fractional Cable EquationRam K. Saxena0Zivorad Tomovski1Trifce Sandev2Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, IndiaDepartment of Mathematics, University of Rijeka, Radmile Matejcic 2, 51000 Rijeka, CroatiaRadiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, MacedoniaIn 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.http://www.mdpi.com/2227-7390/3/2/153fractional cable equationMittag-Leffler functionsH-functionmoments
collection DOAJ
language English
format Article
sources DOAJ
author Ram K. Saxena
Zivorad Tomovski
Trifce Sandev
spellingShingle Ram K. Saxena
Zivorad Tomovski
Trifce Sandev
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Mathematics
fractional cable equation
Mittag-Leffler functions
H-function
moments
author_facet Ram K. Saxena
Zivorad Tomovski
Trifce Sandev
author_sort Ram K. Saxena
title Analytical Solution of Generalized Space-Time Fractional Cable Equation
title_short Analytical Solution of Generalized Space-Time Fractional Cable Equation
title_full Analytical Solution of Generalized Space-Time Fractional Cable Equation
title_fullStr Analytical Solution of Generalized Space-Time Fractional Cable Equation
title_full_unstemmed Analytical Solution of Generalized Space-Time Fractional Cable Equation
title_sort analytical solution of generalized space-time fractional cable equation
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2015-04-01
description 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.
topic fractional cable equation
Mittag-Leffler functions
H-function
moments
url http://www.mdpi.com/2227-7390/3/2/153
work_keys_str_mv AT ramksaxena analyticalsolutionofgeneralizedspacetimefractionalcableequation
AT zivoradtomovski analyticalsolutionofgeneralizedspacetimefractionalcableequation
AT trifcesandev analyticalsolutionofgeneralizedspacetimefractionalcableequation
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