Multiplicity Solutions for Integral Boundary Value Problem of Fractional Differential Systems

• Main Authors: Shiying Song, Yujun Cui
• Format: Article
• Language: English
• Published: Hindawi Limited 2020-01-01
• Series: Discrete Dynamics in Nature and Society
• Online Access: http://dx.doi.org/10.1155/2020/2651845

This paper deals with the existence and multiplicity of solutions for the integral boundary value problem of fractional differential systems: D0+α1u1t=f1t,u1t,u2t,D0+α2u2t=f2t,u1t,u2t,u10=0, D0+β1u10=0, D0+γ1u11=∫01D0+γ1u1ηdA1η,u20=0, D0+β2u20=0, D0+γ2u21=∫01D0+γ2u2ηdA2η,, where fi:0,1×0,∞×0,∞⟶0,∞ is continuous and αi−2<βi≤2,αi−γi≥1,2<αi≤3,γi≥1i=1,2.D0+α is the standard Riemann–Liouville’s fractional derivative of order α. Our result is based on an extension of the Krasnosel’skiĭ’s fixed-point theorem due to Radu Precup and Jorge Rodriguez-Lopez in 2019. The main results are explained by the help of an example in the end of the article.