The numerical solution of linear multi-term fractional differential equations: systems of equations

Authors:
John T. Edwards;Neville J. Ford;A. Charles Simpson
Affiliations:
Mathematics Department, Chester College, Parkgate Road, Chester, CH1 4BJ, UK;Mathematics Department, Chester College, Parkgate Road, Chester, CH1 4BJ, UK;Mathematics Department, Chester College, Parkgate Road, Chester, CH1 4BJ, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 3
Cited 10

Discretized fractional calculus

SIAM Journal on Mathematical Analysis
Convolution quadrature and discretized operational calculus I.

Numerische Mathematik
Numerical methods for ordinary differential systems: the initial value problem

Numerical methods for ordinary differential systems: the initial value problem

An approximate method for numerical solution of fractional differential equations

Signal Processing - Fractional calculus applications in signals and systems
Solving a system of nonlinear fractional differential equations using Adomian decomposition

Journal of Computational and Applied Mathematics
Short memory principle and a predictor-corrector approach for fractional differential equations

Journal of Computational and Applied Mathematics
Numerical analysis for distributed-order differential equations

Journal of Computational and Applied Mathematics
Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

Journal of Computational and Applied Mathematics
Technical communique: A note on fractional-order derivatives of periodic functions

Automatica (Journal of IFAC)
Convergence of the variational iteration method for solving multi-order fractional differential equations

Computers & Mathematics with Applications
On the convergence of spline collocation methods for solving fractional differential equations

Journal of Computational and Applied Mathematics
A method for solving differential equations of fractional order

Journal of Computational and Applied Mathematics
Piecewise polynomial collocation for linear boundary value problems of fractional differential equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.