Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2014; 29(1): 173-185

Printed January 31, 2014

https://doi.org/10.4134/CKMS.2014.29.1.173

Copyright © The Korean Mathematical Society.

A general solution of a space-time fractional anomalous diffusion problem using the series of bilateral eigen-functions

Hemant Kumar, Mahmood Ahmad Pathan, and Harish Srivastava

D.A-V. (P.G.) College Kanpur, Pala Campus Arunapuram, D.A-V. (P.G.) College Kanpur

Abstract

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In the present paper, we consider an anomalous diffusion problem in two dimensional space involving Caputo time and Riesz-Feller fractional derivatives and then solve it by using a series involving bilateral eigen-functions. Also, we obtain a numerical approximation formula of this problem and discuss some of its particular cases.

Keywords: anomalous diffusion problem, Caputo-derivative, Riesz-Feller fractional derivatives, a series of bilateral eigen-functions, numerical approximation formula

MSC numbers: 26A33, 33R11, 60J60, 47B06, 42B05, 33E12, 34K28

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