The Neumann problem for the generalized Bagley-Torvik fractional differential equation

Abstract We discuss the existence and multiplicity of solutions to the generalized Bagley-Torvik fractional differential equation u″ = AcDαu + f (t, u, u′) satisfying the Neumann boundary conditions u′ (0) = u′ (T ) = 0. The solvability of the problem is proved by the combination of the Leray-Schauder degree method with the extremal principle.

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