University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20230812New Fixed Point Results for Some Rational Contraction on $(\phi , \psi)$-Metric Spaces70675210.22130/scma.2023.1971215.1191ENMohammed Mohammed AayedTalebDepartment of Mathematics, Science College, Swami Ramanand Teerth Marathwada University, Nanded-431606, India.0000-0001-9475-4679V. CBorkarDepartment of Mathematics, Yeshwant Mahavidyalaya, Swami Ramanand Teerth Marathwada University, Nanded-431606, India.Journal Article20221022In this article, we define generalized $(\varphi,\sigma,\gamma)$-rational contraction, generalized $(\alpha\beta,\varphi\theta,F)$-rational contraction and establish some new fixed point results in $(\phi,\psi)$-metric space. We also present instances to support our main results. We will use the results we obtained to investigate the existence and uniqueness of solutions to first-order differential equations.