q-Exponential fixed point theorem for mixed monotone operator with q-fractional problem

In this work, we examine the existence and uniqueness(EU) of q-Exponential positive solution (q-EPS) of the hybrid q-fractional boundary value problem (q-FBVP).We prove the q-Exponential fixed point theorem (q-EFPT) with a new set ph, e1 in the Banach space E to check the EU of q-EPS of the q-FBVP. In the long run, an exemplum is given to show the correctness of our results.