Analysis and numerical methods for fractional differential equations with delay

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:252

Article

Morgado, M. L.^1,2  Ford, N. J.³ 

[1] Univ Tras Os Montes & Alto Douro, Cemat, Vila Real, Portugal

[2] Univ Tras Os Montes & Alto Douro, Dept Math, Vila Real, Portugal

[3] Univ Chester, Dept Math, Chester, Cheshire, England

关键词: Fractional differential equations;    Delay differential equations;    Method of steps;    Mittag-Leffler functions;    Initial value problems;   

DOI  :  10.1016/j.cam.2012.06.034

来源: Elsevier

【 摘 要 】

In this paper, we consider fractional differential equations with delay. We focus on linear equations. We summarise existence and uniqueness theory based on the method of steps and we give a theorem on the propagation of derivative discontinuities. We discuss the dependence of the solution on the parameters of the equation and conclude with a numerical treatment and examples based on the adaptation of a fractional backward difference method to the delay case. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free