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# A Numerical Algorithm to Initial Value Problem of Caputo Fractional-Order Differential Equation

[+] Author Affiliations
Lu Bai

Northeastern University, Shenyang, Liaoning, ChinaShenyang University, Shenyang, Liaoning, China

Dingyü Xue

Northeastern University, Shenyang, Liaoning, China

Paper No. DETC2015-46699, pp. V009T07A032; 8 pages
doi:10.1115/DETC2015-46699
From:
• ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
• Volume 9: 2015 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
• Boston, Massachusetts, USA, August 2–5, 2015
• Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
• ISBN: 978-0-7918-5719-9

## abstract

A numerical algorithm is presented to solve the initial value problem of linear and nonlinear Caputo fractional-order differential equations. Firstly, nonzero initial value problem should be transformed into zero initial value problem. Error analysis has been done to polynomial algorithm, the reason has been found why the calculation error of the algorithm is large. A new algorithm called exponential function algorithm is proposed based on the analysis. The obtained fractional-order differential equation is transformed into difference equation. If the differential equation is linear, the obtained difference equation is explicit, the numerical solution can be solved directly; otherwise, the obtained difference equation is implicit, the predictor of the numerical solution can be obtained with extrapolation algorithm, substitute the predictor into the equation, the corrector can be solved. Error analysis has been done to the new algorithm, the algorithm is of first order.

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