On new controlled fuzzy metric space and related fixed point results

In this manuscript, we present a new controlled fuzzy metric type space as an extension of the existing concept of controlled fuzzy metric spaces. We present conditions under which a sequence becomes Cauchy in the setting of the newly defined controlled fuzzy metric space. Further, we extend Banach’s contraction principle by incorporating a new form of contraction criteria and demonstrate various fixed point results. Furthermore, we present non-trivial examples to highlight the benefits of our main findings compared to existing results in the literature. Lastly, we investigate a notable application involving the transformation of solar energy into electrical power through the use of differential equations.