Some Fixed-Point Theorems in <i>b</i>-Dislocated Metric Space and Applications

Abstract

In this article, we prove some fixed-point theorems in b-dislocated metric space. Thereafter, we propose a simple and efficient solution for a non-linear integral equation and non-linear fractional differential equations of Caputo type by using the technique of fixed point.

Keywords

• fixed point
• <i>b</i>-dislocated metric space (simply <i>b</i>-dislocated metric space)
• <i>F</i>-contraction
• non-linear fractional differential equations of Caputo type