Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives

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