Armenian Journal of Mathematics http://www.armjmath.sci.am/index.php/ajm Armenian Journal of Mathematics Armen.J.Math., original research papers, survey articles, areas of mathematics, theoretical mathematics, applications, review articles, short communications, conference proceedings, algorithms, Ph.D and doctoral thesis’s. National Academy of Sciences of Armenia en-US Armenian Journal of Mathematics 1829-1163 Almost $\alpha$-Hardy-Rogers-$F$-contractions and their applications http://www.armjmath.sci.am/index.php/ajm/article/view/276 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p style="text-align: justify;">The aim of this article is to introduce the notion of almost $\alpha$-Hardy-Rogers-$F$-contractions in the partial metric space and utilize it to establish the existence of a unique fixed point. Some examples are given to demonstrate the validity of our main result. Our results generalize classical and newer results in the literature. As an application, we solve the initial value problem of damped harmonic oscillator and a nonlinear fractional differential equation satisfying periodic boundary conditions, which demonstrates the importance of our contraction and provides motivation for such investigations.</p> </div> </div> </div> Anita Tomar Ritu Sharma Copyright (c) 2019 Armenian Journal of Mathematics https://creativecommons.org/licenses/by/4.0 2019-11-15 2019-11-15 11 11 1 19