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Two Collocation Type Methods for Fractional Differential Equations with Non-Local Boundary Conditions

    Mikk Vikerpuur Affiliation

Abstract

A class of non-local boundary value problems for linear fractional differential equations with Caputo-type differential operators is considered. By using integral equation reformulation of the boundary value problem, we study the existence and smoothness of the exact solution. Using the obtained regularity properties and spline collocation techniques, we construct two numerical methods (Method 1 and Method 2) for finding approximate solutions. By choosing suitable graded grids, we derive optimal global convergence estimates and obtain some super-convergence results for Method 2 by requiring additional assumptions on equation and collocation parameters. Some numerical illustrations for verification of theoretical results is also presented.

Keyword : differential equation, non-local boundary conditions, collocation method

How to Cite
Vikerpuur, M. (2017). Two Collocation Type Methods for Fractional Differential Equations with Non-Local Boundary Conditions. Mathematical Modelling and Analysis, 22(5), 654-670. https://doi.org/10.3846/13926292.2017.1355339
Published in Issue
Sep 21, 2017
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