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A Numerical Algorithm to Initial Value Problem of Linear 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. DETC2015-46668, pp. V009T07A027; 9 pages
doi:10.1115/DETC2015-46668
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
  • Copyright © 2015 by ASME

abstract

A numerical algorithm is presented to solve the initial value problem of linear Caputo fractional-order differential equations. Error analysis has been done to Taylor series algorithm, the reason has been found why the error of the algorithm is large, the condition of using Taylor series algorithm is presented. A new algorithm called exponential function algorithm is proposed based on the analysis. Nonzero initial value problem could be transformed into zero initial value problem. The obtained fractional-order differential equation is transformed into difference equation, the numerical solution can be found with closed form solution formula. The error of the numerical solution can be modified with prediction-correction algorithm.

Copyright © 2015 by ASME

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