Document Type : Research Paper
Department of Mathematics, Lovely Professional University, Phagwara, Punjab-144411, India
Department of Mathematics, Government Degree College Thatyur, Tehri Garhwal(Uttrakhand), India
School of Mathematics, Thapar Institute of Engineering & Technology, Patiala-147004, Punjab, India
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.