Anti-periodic boundary value problems of fractional differential equations with the Riemann-Liouville fractional derivative

Advances in Difference Equations

Guoqing Chai¹ 

[1] College of Mathematics and Statistics, Hubei Normal University, Hubei, P.R. China

关键词: fractional differential equations;    anti-periodic boundary value problems;    existence results;    fixed point theorem;   

DOI  :  10.1186/1687-1847-2013-306

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the author puts forward a kind of anti-periodic boundary value problems of fractional equations with the Riemann-Liouville fractional derivative. More precisely, the author is concerned with the following fractional equation:D0+αu(t)=f(t,u(t),u′(t)),t∈(0,1)with the anti-periodic boundary value conditionst2−αu(t)|t→0+=−t2−αu(t)|t=1,(t2−αu(t))|t→0+′=−(t2−αu(t))|t=1′,whereD0+αdenotes the standard Riemann-Liouville fractional derivative of orderα∈(1,2), and the nonlinear functionf(t,⋅,⋅)may be singular att=0. By applying the contraction mapping principle and the other fixed point theorem, the author obtains the existence and uniqueness of solutions. MSC:34A08, 34B15.

【 授权许可】

CC BY