Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays
Joint Authors
Mahdy, A. M. S.
Sweilam, Nasser Hassan
Khidr, M. M.
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-19
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
A numerical method for solving the fractional-order logistic differential equation with two different delays (FOLE) is considered.
The fractional derivative is described in the Caputo sense.
The proposed method is based upon Chebyshev approximations.
The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations.
Special attention is given to study the convergence and the error estimate of the presented method.
Numerical illustrations are presented to demonstrate utility of the proposed method.
Chaotic behavior is observed and the smallest fractional order for the chaotic behavior is obtained.
Also, FOLE is studied using variational iteration method (VIM) and the fractional complex transform is introduced to convert fractional Logistic equation to its differential partner, so that its variational iteration algorithm can be simply constructed.
Numerical experiment is presented to illustrate the validity and the great potential of both proposed techniques.
American Psychological Association (APA)
Sweilam, Nasser Hassan& Khidr, M. M.& Mahdy, A. M. S.. 2012. Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-1029002
Modern Language Association (MLA)
Sweilam, Nasser Hassan…[et al.]. Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays. Journal of Applied Mathematics No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-1029002
American Medical Association (AMA)
Sweilam, Nasser Hassan& Khidr, M. M.& Mahdy, A. M. S.. Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-1029002
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1029002