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

Abstract Under some simple conditions on the coefficient a ( t ), we establish that the initial value problem 0 D t α x ′ + a ( t ) x = 0 , t > 0 , lim t ↘ 0 [ t 1 - α x ( t ) ] = 0 has no solution in L p ( ( 1 , + ∞ ) , R ) , where p - 1 p > α > 1 p and 0 D t α 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.

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