期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 44, 期 -, 页码 460-481出版社
ELSEVIER
DOI: 10.1016/j.cnsns.2016.09.006
关键词
Fractional calculus; Semigroup law; Numerical methods; Population growth model
类别
资金
- Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications
- Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia) [UID/MAT/04106/2013]
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem, Fermat's Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided. (C) 2016 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据