关键词: Boundary value, Laplace transform, Mittage-Leffler function, fractional derivative, Caputo's derivative, fixed point, cone

Abstract:

This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative
$$
\left\{
\begin {array}{l}
_0^{C}D_t^\delta u(t) =g(t,u(t)),\quad 0u(0)=\alpha\neq 0,\quad u(1)=\beta\neq 0.
\end{array}
\right.
$$

Key words: Boundary value, Laplace transform, Mittage-Leffler function, fractional derivative, Caputo's derivative, fixed point, cone