Hamilton-Jacobi fractional mechanics

As a continuation of Rabei et al. work Eqab M. Rabei, Khaled I. Nawafleh, Raed S. Hijjawi, Sami I. Muslih, Dumitru Baleanu, The Hamilton formalism with fractional derivatives, J. Math. Anal. Appl. 327 (2007) 891-897], the Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton-Jacobi function in configuration space is obtained in a similar manner to the usual mechanics. Two problems are considered to demonstrate the application of the formalism. The result is found to be in exact agreement with Agrawal's formalism.