\(\psi \)-Tempered fractional differential equations with impulses

In this paper, we study variational structure for the \(\psi \) $\psi$ -Tempered fractional derivatives operator. We investigate some properties of \(\psi \) $\psi$ -Tempered fractional integral and derivative which are used of variational structure. Also, the existence of solutions for a problem with \(\psi \) $\psi$ -Tempered fractional derivative is proved by applying variational methods and critical point theory. Finally, an example is provided.