Fixed point results with applications to nonlinear fractional differential equations

The aim of this paper is to define a Berinde type ($ \rho $, $ \mu $)-$ \vartheta $ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation.