ITM Web Conf.
Volume 29, 20191st International Conference on Computational Methods and Applications in Engineering (ICCMAE 2018)
|Number of page(s)||8|
|Published online||15 October 2019|
Functions represented into fractional Taylor series
Technical University of Civil Eng. of Bucharest, Department of Mathematics and Computer Science
Fractional Taylor series are studied. Then solutions of fractional linear ordinary differential equations (FODE), with respect to Caputo derivative, are approximated by fractional Taylor series. The Cauchy-Kowalevski theorem is proved to show the existence and uniqueness of local solutions for FODE with Cauchy initial data. Sufficient conditions for the global existence of the solution and the estimate of error are given for the method using fractional Taylor series. Two illustrative numerical examples are given to demonstrate the validity and applicability of this method.
© The Authors, published by EDP Sciences, 2019
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