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 $$ with mixed non-linearities of the form satisfying the Dirichlet boundary conditions $$ , 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.