Electron. J. Differential Equations, Vol. 2016 (2016), No. 249, pp. 1-14.

Riemann-Liouville fractional cosine functions

Zhan-Dong Mei, Ji-Gen Peng

Abstract:
In this article, we present the notion of Riemann-Liouville fractional cosine function. we prove that a Riemann-Liouville alpha-order fractional cosine function is equivalent to the Riemann-Liouville alpha-order fractional resolvent introduced in [15].

Submitted June 7, 2015. Published September 16, 2016.
Math Subject Classifications: 33E12.
Key Words: Riemann-Liouville fractional cosine function; fractional resolvent; fractional differential equation.

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Zhan-Dong Mei
School of Mathematics and Statistics
Xian Jiaotong University
Xian 710049, China
email: zhdmei@mail.xjtu.edu.cn
Ji-Gen Peng
School of Mathematics and Statistics
Xian Jiaotong University
Xian 710049, China
email: jgpeng@mail.xjtu.edu.cn

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