Spline Collocation for Multi-Term Fractional Integro-Differential Equations with Weakly Singular Kernels

We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study the existence, uniqueness and regularity of the exac...

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Bibliographic Details
Published inFractal and fractional Vol. 5; no. 3; p. 90
Main Authors Pedas, Arvet, Vikerpuur, Mikk
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2021
Subjects
Banach spaces
Boundary conditions
boundary value problem
Boundary value problems
caputo derivative
Collocation
collocation method
Differential equations
Exact solutions
fractional differential equation
graded grid
Integral equations
Kernels
Numerical analysis
Regularity
Viscoelasticity
weakly singular kernel
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ISSN2504-3110
2504-3110
DOI10.3390/fractalfract5030090

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Summary:We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study the existence, uniqueness and regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the problem is discussed. Optimal global convergence estimates are derived and a superconvergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract5030090