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.