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This paper is devoted to study the nonlinear sequential fractional boundaryvalue problems involving generalized $\psi$-Caputo fractional derivatives withnonlocal boundary conditions. We investigate the Green function and some of itsproperties, from which we obtain a new Lyapunov-type inequality for ourproblem. A lower bound for the possible eigenvalues of our problem is derived.Furthermore, we apply some properties of the Green function to obtain someexistence results for our problem. It is worth mentioning that our resultsstill work with some source functions including singularities.

Nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives