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In this article, we introduce the notion of cyclic $α$-admissible mapping with respect to $θ$ with its special cases, which are cyclic $α$-admissible mapping with respect to $θ^∗$ and cyclic $α^∗$-admissible mapping with respect to $θ.$ We present the notion of orthogonal $(αθ−βF)$-rational contraction and establish new fixed point results over orthogonal $\mathcal{F}$-metric space. The study includes illustrative examples to support our results. We apply our results to prove the existence and uniqueness of solutions for second-order differential equations.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.825}, url = {http://global-sci.org/intro/article_detail/jnma/23365.html} }In this article, we introduce the notion of cyclic $α$-admissible mapping with respect to $θ$ with its special cases, which are cyclic $α$-admissible mapping with respect to $θ^∗$ and cyclic $α^∗$-admissible mapping with respect to $θ.$ We present the notion of orthogonal $(αθ−βF)$-rational contraction and establish new fixed point results over orthogonal $\mathcal{F}$-metric space. The study includes illustrative examples to support our results. We apply our results to prove the existence and uniqueness of solutions for second-order differential equations.