
New Fixed Point Results over Orthogonal $\mathcal{F}$Metric Spaces and Application in SecondOrder Differential Equations 

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KeyWord:Fixed point, orthogonal $(\alpha\theta\beta F)$rational contraction, cyclic $\alpha$admissible mapping with respect to $\theta$, orthogonal $\mathcal{F}$metric space, secondorder differential equation 
Author Name  Affiliation  Mohammed M.A. Taleb  Department of Mathematics, Science College, Swami Ramanand Teerth Marathwada University, Nanded431606, India Department of Mathematics, Hodeidah University, P.O. Box 3114, AlHodeidah, Yemen  Saeed A.A. AlSalehi  Department of Mathematics, Science College, Swami Ramanand Teerth Marathwada University, Nanded431606, India Department of Mathematics, Aden University, P.O. Box 124, Aden, Yemen  V.C. Borkar  Department of Mathematics, Yeshwant Mahavidyalaya, Swami Ramanand Teerth Marathwada University, Nanded431606, India 

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Abstract: 
In this article, we introduce the notion of cyclic $\alpha$admissible mapping with respect to $\theta$ with its special cases, which are cyclic $\alpha$admissible mapping with respect to $\theta^*$ and cyclic $\alpha^*$admissible mapping with respect to $\theta$. We present the notion of orthogonal $(\alpha\theta\beta F)$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 secondorder differential equations. 


