Almost $\alpha$-$F$-contraction, fixed points and applications

Document Type : Research Paper


1 Department of Mathematics, Lovely Professional University, Phagwara, Punjab-144411, India

2 Department of Mathematics, Government Degree College Thatyur, Tehri Garhwal(Uttrakhand), India

3 School of Mathematics, Thapar Institute of Engineering & Technology, Patiala-147004, Punjab, India

4 Department of Mathematics, G. I. C. Gheradhar (Dogi) Tehri Garhwal (Uttrakhand), India


In this manuscript, we initiate an almost $\alpha$-$F$-contraction and an almost $\alpha$-$F$- weak contraction in the setting of partial metric spaces and establish adequate conditions for the presence of fixed points. The obtained results generalize the classical and recent results of the literature, which are validated by suitable examples. As applications of these established results, we solve a nonlinear fractional differential equation and a boundary value problem.