# Almost $\alpha$-Hardy-Rogers-$F$-contractions and their applications

Tomar, Anita and Sharma, Ritu (2015) Almost $\alpha$-Hardy-Rogers-$F$-contractions and their applications. Armenian Journal of Mathematics, 11 (11). pp. 1-19. ISSN 1829-1163

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## Abstract

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.

Item Type: Article $\alpha$-admissible, $0$-complete, almost $\alpha$-Hardy-Rogers-$F$-contraction, partial metric space 41-xx Approximations and expansions 852 Professor Anry Nersesyan 10 Dec 2019 22:16 26 Dec 2019 20:29

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