ITM Web Conf.
Volume 20, 2018International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|Number of page(s)
|Numerical and Applied Analysis
|12 October 2018
A numerical scheme for problems in fractional calculus
Department of Mathematics and Statistics, Mississippi state University, Mississippi State, MS 39762, USA
In this paper, a new numerical method for solving the fractional differential equations with boundary value problems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the boundary value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Key words: Hybrid functions / fractional-order differential equations / block-pulse / Bernoulli polynomials / Caputo derivative / numerical solution
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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