The Hamilton formalism with fractional derivatives

• Published in: Journal of mathematical analysis and applications Vol. 327; no. 2; pp. 891 - 897
• Main Authors: Rabei, Eqab M., Nawafleh, Khaled I., Hijjawi, Raed S., Muslih, Sami I., Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15-03-2007; Elsevier
• Subjects: Calculus of variations and optimal control; Exact sciences and technology; Fractional derivatives; Lagrangian and Hamiltonian formulation; Mathematical analysis; Mathematics; Real functions; Sciences and techniques of general use; Fractional derivatives; Lagrangian and Hamiltonian formulation; Equation of motion; Mathematical analysis; Hamilton equation; Variational calculus; Fractional derivative
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2006.04.076

Recently the traditional calculus of variations has been extended to be applicable for systems containing fractional derivatives. In this paper the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. The Hamilton's equations of motion are obtained in a similar manner to the usual mechanics. In addition, the classical fields with fractional derivatives are investigated using Hamiltonian formalism. Two discrete problems and one continuous are considered to demonstrate the application of the formalism, the results are obtained to be in exact agreement with Agrawal's formalism.