Modified Meir-Keeler-type contraction in fuzzy metric spaces for single-valued and set-valued mappings with solution to boundary value problem

In this work, the revised conceptions of single-valued and set-valued Meir-Keeler-type contraction are defined, together with fixed point findings for such contractions in fuzzy metric space ( $\mathcal{FMS}$ ). Extensive examples are provided to validate the outcomes. The findings demonstrated in this work generalize a number of intriguing findings in existing metric spaces. Our novel thoughts and results are also applied to the folding of an elastic band restrained at both ends by taking into account the two-point boundary issue involving differential equations of fourth order.