Fractional differential equations with integral boundary conditions. (English) Zbl 1312.34028
From the introduction: We consider the following integral boundary value problem for nonlinear fractional differential equation:
\[
\begin{gathered} D^q x(t)= f(t,x(t)),\quad t\in J= [0,T],\;T> 0,\\ x(0)=\lambda \int^T_0,\\ x(s)\,ds+ d,\quad d\in\mathbb R,\end{gathered}
\]
where \(f\in C(J\times\mathbb R,\mathbb R)\), \(\lambda\geq 0\) and \(0<q<1\).
The lower and upper solutions combined with monotone iterative technique is applied. Problems of existence and unique solutions are discussed.
The lower and upper solutions combined with monotone iterative technique is applied. Problems of existence and unique solutions are discussed.
MSC:
34A08 | Fractional ordinary differential equations |
34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
34A45 | Theoretical approximation of solutions to ordinary differential equations |