On existence of fixed points and applications to a boundary value problem and a matrix equation in C^*−algebra valued partial metric spaces

We utilize Hardy-Rogers contraction and CJM−contraction in a C^*−algebra valued partial metric space to create an environment to establish a fixed point.

Next, we present examples to elaborate on the novel space and validate our result. We conclude the paper by solving a boundary value problem and a matrix equation as applications of our main results which demonstrate the significance of our contraction and motivation for such investigations.