IJPAM: Volume 90, No. 1 (2014)

NUMERICAL SOLUTION OF FRACTIONAL DELAY
DIFFERENTIAL EQUATIONS USING SPLINE FUNCTIONS

Mahmoud N. Sherif$^1$, Ibrahim Abouelfarag$^2$, T.S. Amer$^3$
$^1$Department of Mathematics
Faculty of Science
Menoufia University
Shebeen El Koom, EGYPT
$^2$Department of Mathematics
Faculty of Science
Suez Canal University
Ismailia, EGYPT
$^3$Department of Mathematics
Faculty of Science
Tanta University
Tanta, EGYPT
$^{1,2,3}$Department of Mathematics
Faculty of Science and Education
Taif University
Al-Khurmah Branch, Taif, KSA


Abstract. In this paper, we investigate the use of suitable spline functions of polynomial form to approximate the solution of fractional delay differential equations. The description of the proposed approximation method is first introduced. The error analysis and stability of the method are theoretically investigated. The proposed spline function is an extension and generalization to the polynomial spline functions used in [15]. Numerical example is given to illustrate the applicability, accuracy and stability of the proposed method.

Received: October 26, 2013

AMS Subject Classification: 65L07, 34A08, 34A45

Key Words and Phrases: fractional delay differential equation, Spline functions, Taylor expansion, stability

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DOI: 10.12732/ijpam.v90i1.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 1