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Abstract. In this work we study the fractional forced pendulum equation with combined fractional derivatives. Using minimization techniques form variational calculus we show that (0.1) has a nontrivial solution.

In this work, we study the existence of positive solutions for a class of fractional differential equation given bywhere˛2 .1=2, 1/, t 2 R, u 2 R, f 2 C.R, R/. Using the mountain pass theorem and comparison argument, we prove that (1) at least has one nontrivial solution.