Abstract:

We studied a positive solution of the semipositone boundary value problem of fractional differential equation:
D^α₀₊u(t)=λf(t,u(t)),0         u(0)=u(1)=u′(0)=u′(1)=0
 where 3<α≤4 is a real number, and D^α₀₊ is the standard RiemannLiouville differentiation, and the nonlinear term has no numerical lower bound. We gave an existence theorem of this equation by means of the Krasnosel’skii fixedpoint theorem on a cone.

Key words: fractional differential equation, boundaryvalue problem, positive solution, existence theorem, fixedpoint theorem