On the uniqueness of solutions for a class of fractional differential equations

Abstract We are concerned with the uniqueness of solutions for the following nonlinear fractional boundary value problem: D p x ( t ) + f ( t , x ( t ) ) = 0 , 2 p ≤ 3 , t ∈ ( 0 , 1 ) , x ( 0 ) = x ′ ( 0 ) = 0 , x ( 1 ) = 0 where D 0 + p denotes the standard Riemann–Liouville fractional derivative. Our analysis relies on the theory of linear operators and the ‖ ⋅ ‖ e norm.

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