Multiplicity Solutions for Integral Boundary Value Problem of Fractional Differential Systems
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,∞ i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/2651845 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |