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Space- and Time-Fractional Legendre-Pearson Diffusion Equation

[+] Author Affiliations
Malgorzata Klimek

Czestochowa University of Technology, Czestochowa, Poland

Om Prakash Agrawal

Southern Illinois University, Carbondale, IL

Paper No. DETC2013-12604, pp. V004T08A019; 7 pages
doi:10.1115/DETC2013-12604
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME

abstract

In this paper we study space- and time-fractional diffusion equations called Fractional Legendre-Pearson Diffusion Equations (FLPDEs) in finite space interval. We define the space fractional part using Fractional Legendre Operators and the time fractional part using Fractional Caputo derivative. We consider both the standard and symmetrized versions of FLPDEs. For both equations, we use the method of integral Legendre transform and inverse integral Legendre transform to solve the two equations. The solutions are given in the form of infinite series containing Legendre polynomials dependent on the space variable and Mittag-Leffler functions dependent on time. We demonstrate that these series are convergent. The simplicity with which the solutions of the FLPDEs are obtained in closed form should initiate further research in this field.

Copyright © 2013 by ASME

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