Journal of Integral Equations and Applications

A hybrid collocation method for fractional initial value problems

Linjun Wang, Fang Wang, and Yanzhao Cao

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Abstract

This paper is concerned with the application of a hybrid collocation method to a class of initial value problems for differential equations of fractional order. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with a weakly singular kernel. Then, the Volterra integral equation is converted to a fixed point problem. A hybrid collocation algorithm is developed to solve the fixed point problem, and the optimal order of convergence of the proposed algorithm is obtained. Two numerical experiments are conducted to demonstrate the efficiency of the hybrid collocation algorithm.

Article information

Source
J. Integral Equations Applications, Volume 31, Number 1 (2019), 105-129.

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1561601028

Digital Object Identifier
doi:10.1216/JIE-2019-31-1-105

Mathematical Reviews number (MathSciNet)
MR3974985

Zentralblatt MATH identifier
07080017

Subjects
Primary: 26A33: Fractional derivatives and integrals 45G10: Other nonlinear integral equations 65L05: Initial value problems

Keywords
Fractional initial value problem hybrid collocation method weakly singular kernel convergence order.

Citation

Wang, Linjun; Wang, Fang; Cao, Yanzhao. A hybrid collocation method for fractional initial value problems. J. Integral Equations Applications 31 (2019), no. 1, 105--129. doi:10.1216/JIE-2019-31-1-105. https://projecteuclid.org/euclid.jiea/1561601028


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