Abstract:

We used the fixed point theorem of cone expansion and cone compression to study the eigenvalue problem of nonlinear fractional differential equation so as to obtain the existence of positive solutions. The results show that for a type of αorder fractional differential equation eigenvalue problem (3<α≤4), the differential equation has at least one positive solution when eigenvalue parameter belongs to an open interval.

Key words: fractional differential equation, positive solution, eigenvalue problem, fixed point theorem