Results for nonlinear fractional differential equations on pseudo-metric spaces with three boundary values

In this paper, we investigate the existence of solutions in Gauge spaces for the nonlinear fractional differential equation boundary value problem+u(t) + f(t, u(t)) = 0, t [O, T] (1.1)with different boundary value u(O) = u(T) = 0 and u(O) = u(μ) , u(T) = u(μ) and different order 1 < a 2 and 0 < a < 1. where 0 < /31 < /32 < T and μ [O, T]and + is the standard Riemann-Liouville differentiation with f(t, u(t)) C([O, T] x [O, ), R). By using some fixed-point results on gauge spaces, some existence results of positive solutions are obtained.

Keywords:

Boundary value problem , Fixed point , Fractional differential equation , Green function , Positive solution