On Lp-solutions for a class of sequential fractional differential equations

Under some simple conditions on the coefficient a(t), we establish that the initial value problem 0Dtαx′+a(t)x=0,t>0,limt↘0[t1-αx(t)]=0 has no solution in Lp((1,+∞),R), where p-1p>α>1p and 0Dtα designates the Riemann-Liouville derivative of order α. Our result might be useful for developing a non-integer variant of H. Weyl's limit-circle/limit-point classification of differential equations.