Fractional Euler-Lagrange Equations of Motion in Fractional Space

Abstract

Fractional variational principles have gained considerable importance during the last decade due to their various applications in several areas of science and engineering. In this study, the fractional Euler-Lagrange equations corresponding to a prescribed fractional space are obtained. These equations are obtained using the traditional method of calculus of variations adapted to the case of fractional space. The most general fractional Lagrangian is considered and the limit case when the parameters involved in fractional derivatives are equal to one, is obtained. Two examples are investigated in this study, namely the free particle on fractional space and the fractional simple pendulum, and their corresponding fractional Euler-Lagrange equations ar obtained.