Su, Xinwei; Zhang, Shuqin Solutions to boundary-value problems for nonlinear differential equations of fractional order. (English) Zbl 1173.34011 Electron. J. Differ. Equ. 2009, Paper No. 26, 15 p. (2009). Summary: We discuss the existence, uniqueness and continuous dependence of solutions for a boundary value problem of nonlinear fractional differential equation.We present the analysis of the boundary value problem\[ \begin{gathered} ^CD^\alpha_{0^+}u(t)=f(t,u(t),{}^CD^\beta_{0^+}u(t)), \quad 0<t<1,\\ a_1u(0)-a_2u'(0)=A,\;b_1u(1)+b_2u'(1)=B,\tag{1}\end{gathered} \]where \(1<\alpha\leq 2\), \(0<\beta\leq 1\), \(a_ib_i\geq 0\), \(i=1,2\), \(a_1b_1+a_1b_2+a_2b_1>0\), \(^CD^\alpha_{0+}\) and \(^CD^\beta_{0^+}\) are the Caputo’s fractional derivatives and \(f:[0,1]\times\mathbb R\times \mathbb R\to\mathbb R\) is continuous. We impose a growth condition on the function \(f\) to prove an existence result for (1). Cited in 14 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 26A33 Fractional derivatives and integrals 47N20 Applications of operator theory to differential and integral equations Keywords:boundary value problem; fractional derivative; fixed-point theorem; Green’s function; existence and uniqueness; continuous dependence PDFBibTeX XMLCite \textit{X. Su} and \textit{S. Zhang}, Electron. J. Differ. Equ. 2009, Paper No. 26, 15 p. (2009; Zbl 1173.34011) Full Text: EuDML EMIS