Bashir Ahmad

Existence Results for Multi-Point Nonlinear Boundary Value Problems for Fractional Differential Equations

abstract:
In this paper, we obtain some existence results in a Banach space for a multi-point boundary value problem involving a nonlinear fractional differential equation given by
\begin{gather*}
^cD^qx(t)=f(t,x(t)), \;\;\; 0<t<1, \;\;1 < q \le 2, \\ \alpha_1 x(0)- \beta_1 x'(0) = \gamma_1 x(\eta_1), \;\;\; \alpha_2 x(1)+ \beta_2 x'(1) = \gamma_2 x(\eta_2), \;\; 0<\eta_1,\eta_2<1.
\end{gather*}
Our results are based on contraction mapping principle and Krasnoselskii's fixed point theorem.

Mathematics Subject Classification: 34A34, 34B15

Key words and phrases: Nonlinear fractional differential equations, multi-point boundary conditions, existence, fixed point theorem