## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Numerical evaluation of order six for fractional differential equations : stability and convergency

#### Abstract

In this paper, a novel high-order numerical method is formulated to solve fractional differential equations. The fractional derivative is described in the Caputo sense due to its applicability to real-world phenomena. First, the fractional differential equation is reduced into a Volterra-type integral equation by applying the Laplace and inverse Laplace transform. Then, the piecewise Lagrange interpolation polynomial of degree five is utilized to approximate unknown function. The truncation error estimates for the novel schemes is derived, and it is theoretically established that the order of convergence of the numerical method is $O(h^6)$. The stability analysis of the novel method is also carefully investigated. Numerical examples are given to show the accuracy, applicability and the effectiveness of the novel method.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 2 (2019), 203-221.

Dates
First available in Project Euclid: 28 June 2019

https://projecteuclid.org/euclid.bbms/1561687562

Digital Object Identifier
doi:10.36045/bbms/1561687562

Mathematical Reviews number (MathSciNet)
MR3975825

Zentralblatt MATH identifier
07094825

#### Citation

Asl, Mohammad Shahbazi; Javidi, Mohammad. Numerical evaluation of order six for fractional differential equations : stability and convergency. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 2, 203--221. doi:10.36045/bbms/1561687562. https://projecteuclid.org/euclid.bbms/1561687562