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High Order Approximations of Solutions to Initial Value Problems for Linear Fractional Integro-Differential Equations
Ford, Neville J. Pedas, Arvet Vikerpuur, Mikk
Ford, Neville J.
Pedas, Arvet
Vikerpuur, Mikk
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2023-07-17
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Abstract
We consider a general class of linear integro-differential equations with Caputo fractional derivatives and weakly singular kernels. First, the underlying initial value problem is reformulated as an integral equation and the possible singular behavior of its exact solution is determined. After that, using a suitable smoothing transformation and spline collocation techniques, the numerical solution of the problem is discussed. Optimal convergence estimates are derived and a superconvergence result of the proposed method is established. The obtained theoretical results are supported by numerical experiments.
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Ford, N. J., Pedas, A., & Vikerpuur, M. (2023). High order approximations of solutions to initial value problems for linear fractional integro-differential equations. Fractional Calculus and Applied Analysis, 26, 2069–2100. https://doi.org/10.1007/s13540-023-00186-9
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Springer
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Fractional Calculus and Applied Analysis
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Article
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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s13540-023-00186-9
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1311-0454
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1314-2224