<p>This paper investigates the general right fractional calculus as well as applications to Euler–Lagrange equations and terminal value problems. A general <i>Q</i> operator is introduced to give fundamental theorems of the general right fractional calculus by use of the duality of the left one. Then Riesz space derivative is defined by the left and right fractional derivatives. Parseval relations are presented and a class of general fractional Euler–Lagrange equations is given. Finally, the <i>Q</i> operator is used to solve linear terminal value problems. It can be concluded that the <i>Q</i> operator is well defined and provides a new and easy approach to propositions of the right fractional calculus.</p>