We state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order α∈(1,2]\documentclass[12pt]{minimal}
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\begin{document}$\alpha \in (1,2]$\end{document} with mixed non-linearities of the form
(Tαax)(t)+r1(t)|x(t)|η−1x(t)+r2(t)|x(t)|δ−1x(t)=g(t),t∈(a,b),\documentclass[12pt]{minimal}
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\begin{document}$$ \bigl(\mathbf{T}_{\alpha }^{a} x\bigr) (t)+r_{1}(t) \bigl\vert x(t) \bigr\vert ^{\eta -1}x(t)+r_{2}(t)\bigl\vert x(t) \bigr\vert ^{ \delta -1}x(t)=g(t), \quad t\in (a,b), $$\end{document} satisfying the Dirichlet boundary conditions x(a)=x(b)=0\documentclass[12pt]{minimal}
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\begin{document}$x(a)=x(b)=0$\end{document}, where r1\documentclass[12pt]{minimal}
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\begin{document}$r_{1}$\end{document}, r2\documentclass[12pt]{minimal}
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\begin{document}$r_{2}$\end{document}, and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0<η<1<δ<2\documentclass[12pt]{minimal}
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\begin{document}$0<\eta <1<\delta <2$\end{document}. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative Tαa\documentclass[12pt]{minimal}
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\begin{document}$\mathbf{T}_{\alpha }^{a}$\end{document} is replaced by a sequential conformable derivative Tαa∘Tαa\documentclass[12pt]{minimal}
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\begin{document}$\mathbf{T}_{\alpha }^{a} \circ \mathbf{T}_{\alpha }^{a}$\end{document}, α∈(1/2,1]\documentclass[12pt]{minimal}
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\begin{document}$\alpha \in (1/2,1]$\end{document}. The potential functions r1\documentclass[12pt]{minimal}
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\begin{document}$r_{1}$\end{document}, r2\documentclass[12pt]{minimal}
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\begin{document}$r_{2}$\end{document} as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.
