Applications to boundary value problems and homotopy theory via tripled fixed point techniques in partially metric spaces

In this manuscript, some tripled fixed point results were derived under (ϕ, ρ, ℓ)-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory.