## Abstract and Applied Analysis

### Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

#### Abstract

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinearfractional differential equations. The proposed method is applicable for $0<\alpha \le 1$ and $\alpha \ge 1$, where $\alpha$ denotes the order of the fractional derivative in the Caputo sense. The results obtainedare in good agreement with the exact analytical solutions and the numerical results presentedelsewhere. Results also show that the technique introduced here is robust and easy to apply.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 426514, 9 pages.

Dates
First available in Project Euclid: 1 April 2013

https://projecteuclid.org/euclid.aaa/1364845171

Digital Object Identifier
doi:10.1155/2012/426514

Mathematical Reviews number (MathSciNet)
MR2898040

Zentralblatt MATH identifier
1235.65015

#### Citation

Al-Rabtah, Adel; Momani, Shaher; Ramadan, Mohamed A. Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 426514, 9 pages. doi:10.1155/2012/426514. https://projecteuclid.org/euclid.aaa/1364845171

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