In the present research article, the notion of hesitant fuzzy mapping, contraction hesitant fuzzy mapping, generalized contraction of hesitant fuzzy mapping are introduced in setting of extended b-metric structure, which in particular case reduced to b-metric space. The newly introduced concepts are used to prove hesitant fuzzy fixed point theorems. The main results have extended and unified recent results in literature. The results are validated with the help of examples. Finally, as an application, the results are applied to solve integral equation of fredholm type.