文章基本信息

标题：Existence of solutions for fractional differential equations with integral boundary conditions
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作者：Rian Yan ; Shurong Sun ; Hongling Lu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：25
DOI：10.1186/1687-1847-2014-25
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study boundary-value problems for the following nonlinear fractional differential equations involving the Caputo fractional derivative: D 0 + α C x ( t ) = f ( t , x ( t ) , C D 0 + β x ( t ) ) , t ∈ [ 0 , 1 ] , x ( 0 ) + x ′ ( 0 ) = y ( x ) , ∫ 0 1 x ( t ) d t = m , x ″ ( 0 ) = x ‴ ( 0 ) = ⋯ = x ( n − 1 ) ( 0 ) = 0 , where D 0 + α C , D 0 + β C are the Caputo fractional derivatives, f : [ 0 , 1 ] × R × R → R is a continuous function, y : C ( [ 0 , 1 ] , R ) → R is a continuous function and m ∈ R , n − 1 < α < n ( n ≥ 2 ), 0 < β < 1 is a real number. By means of the Banach fixed-point theorem and the Schauder fixed-point theorem, some solutions are obtained, respectively. As applications, some examples are presented to illustrate our main results. MSC:34A08, 34B10.
关键词：fractional differential equation ; boundary-value problem ; fixed-point theorem