A FITE TYPE RESULT FOR SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS

Given the solution f of the sequential fractional differential equation

_aD^α_t ( _aD^α_t f ) + P( t ) f = 0, t ∈ [b, c],    where   −∞ < a < b < c < +∞, α ∈ (1/ 2 , 1)    and   P : [a, +∞) → [ 0, P_∞], P_∞ < +∞,    is continuous. Assume that there exist   t₁, t₂ ∈ [b, c]  such that  f( t₁ ) = (_aD^α_t f )( t₂ ) = 0. Then, we establish here a positive lower bound for c − a which depends solely on α, P_∞. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.