On positive solutions of certain singular fractional differential equations in orthogonal metric spaces

This article aims to discuss an existence and uniqueness theorem regarding the positive solutions of certain boundary value problems associated with a singular fractional differential equations by fixed point theorems in orthogonal metric spaces. To achieve our goal, we define the orthogonal Geraghty contractions in the context of complete orthogonal metric spaces and utilize the same to prove fixed point theorems for such contractions. In this way, we consolidate and amend innumerable celebrated results in fixed point theory. We provide a non-trivial example to show the legitimacy of the established results.