A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations release_dvrddji6q5blhokij2p3kq4gpm

by Er Gao, Songhe Song, Xinjian Zhang

Published in Mathematical Problems in Engineering by Hindawi Limited.

2012   Volume 2012, p1-11

Abstract

We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>q</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn mathvariant="normal">1,2</mml:mn><mml:mo stretchy="false">]</mml:mo></mml:math>based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the<jats:italic>n</jats:italic>-term approximation. At the same time, the<jats:italic>n</jats:italic>-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.
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