Liu, Xiping; Jia, Mei; Wu, Baofeng Existence and uniqueness of solution for fractional differential equations with integral boundary conditions. (English) Zbl 1201.34010 Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 69, 10 p. (2009). Summary: This paper is devoted to existence and uniqueness of solutions for fractional differential equations with integral boundary conditions. \[ \begin{cases} ^CD^\alpha x(t)+f(t,x(t),x'(t))=0,\quad & t\in(0,1),\\ x(0)=\int^1_0 g_0(s,x(s))\,\mathrm{d}s ,\\ x(1)=\int^1_0 g_1(s,x(s))\,\mathrm{d}s ,\\ x^{(k)}(0)=0,\,\;k=2,3,\dots, [\alpha]-1.\end{cases} \]By means of the Banach contraction mapping principle, some new results on existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for existence and uniqueness of solutions depend on the order \(\alpha\). Cited in 10 Documents MSC: 34A08 Fractional ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations Keywords:Caputo derivative; fractional differential equations; integral boundary conditions; Banach contraction mapping principle; existence and uniqueness PDFBibTeX XMLCite \textit{X. Liu} et al., Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 69, 10 p. (2009; Zbl 1201.34010) Full Text: DOI EuDML EMIS