Solving a fractional differential equation via θ-contractions in ℜ-complete metric spaces

Abstract

In this manuscript, we introduce the notion of ℜα-θ-contractions and prove some fixed-point theorems in the sense of ℜ-complete metric spaces. These results generalize existing ones in the literature. Also, we provide some illustrative non-trivial examples and applications to a non-linear fractional differential equation.

Keywords

• ℜ-metric space
• fixed point results
• non-linear fractional differential equation