We state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order with mixed non-linearities of the form satisfying the Dirichlet boundary conditions , where , , and g are real-valued integrable functions, and the non-linearities satisfy the conditions . Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative is replaced by a sequential conformable derivative , . The potential functions , as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.

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a b s t r a c tIn this paper we give new oscillation criteria for forced super-and sub-linear differential equations by means of nonprincipal solutions.

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