In 1984, Khan et al.  established some fixed point theorems in complete and compact metric spaces by using altering distance functions. In 2017, Gordji et al.  described the notion of orthogonal set and orthogonal metric spaces. In their work, they held a generalization of Banach fixed point theorem in this interestingly-defined construction and in addition, applied their acquired results to demonstrate the existence of a solution of an ordinary differential equation. In this paper, some fixed point theorems on orthogonal metric spaces via altering distance functions inspired by  and  are presented.