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This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations:  μ τ = ∫ 0 τ Γ τ , v , μ v d v and  ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all  μ ∈ U ,  v ∈ 0 , η , and  0 &lt; η ∈ ℝ , where  U = C 0 , η , ℝ is the space of all  ℝ -valued continuous functions on the interval  0 , η and  Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .

Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations