On a Difference Scheme for Solving Cauchy Problems wuth the Caputo Fractional Derivative in a Banach Space
Numerical Analysis
2017-12-11 v1
Abstract
We construct and study a time--semidiscretization scheme for the Cauchy problem associated with a linear homogeneous differential equation with the Caputo fractional time derivative of order and a spatial sectorial operator in a Banach space. For this scheme, we obtain rate--of--convergence and error estimates in terms of the discretization step. We use properties of Mittag--Leffler functions, hypergeometric functions, and the calculus of sectorial operators in a Banach space. Results of numerical experiments are also reported.
Keywords
Cite
@article{arxiv.1712.03047,
title = {On a Difference Scheme for Solving Cauchy Problems wuth the Caputo Fractional Derivative in a Banach Space},
author = {M. M. Kokurin},
journal= {arXiv preprint arXiv:1712.03047},
year = {2017}
}