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Home  >  Volume 31 (July 2015)

Comparative Analysis of Approximation Rules for Computing the Caputo Fractional Derivatives of Functions by Terhemen Aboiyar and Sunday Simon Isah (Pages 347-362)
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Abstract

In this paper, we propose two numerical methods for computing the Caputo fractional derivatives of functions by a weighted sum of function values at specified points. The first algorithm uses modified Trapezoidal rule in conjunction with a forward difference formula while the second algorithm uses the modified Trapezoidal rule in combination with a backward difference formula. Both the forward and backward difference formulas are of the second order. The error analysis for the approximation rules are presented. The approximation rules are implemented in MATLAB through some illustrative examples. Absolute errors are estimated and the orders of accuracy for the approximation rules are computed. The numerical experiments confirmed that all the approximation rules are accurate, efficient and readily implementable.

Keywords: Fractional integral; Trapezoidal Rule; Modified Trapezoidal Rule; Caputo Fractional Derivative.

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