Armenian Journal of Mathematics, 11(11)
2022; 1–19
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Almost α -Hardy-Rogers- F -contractions and their applications

Anita Tomar*, Ritu Sharma

Received: 2024-12-11 · Published: 2022-09-15

© 2022 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Almost α -Hardy-Rogers- F -contractions and their applications
Authors
Anita Tomar, Ritu Sharma
Source journal
Armenian Journal of Mathematics, 11(11)
Published
2022-09-15
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2019.11.11-1-19

Abstract

The aim of this article is to introduce the notion of almost αα-Hardy-Rogers-FF-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.
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