The present manuscript is concerned with the existence and uniqueness of solutions along with the UH-Rassias stability for fractional q-differential Duffing problem having sequential fractional q-derivatives. We make use Banach's and Schaefer's fixed point theorems to prove the uniqueness and the existence of at least one solution for the introduced problem. Also, we discuss the UH-Rassias stability for the mentioned problem. Finally, we give some examples to illustrate the proposed main results.

The authors are grateful to the reviewers for their meticulous reading and suggestions which improved the presentation of the paper. Also, the authors are thankful to the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University for supporting this work with project number (PNURSP2023R27).