Towards a combined fractional mechanics and quantization

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• 作者：Agnieszka B. Malinowska (1) a.malinowska@pb.edu.pl
  Delfim F. M. Torres (2) delfim@ua.pt
• 关键词：Key Words and Phrases fractional canonical formalism – ; Hamiltonian approach – ; variational principles of physics – ; nonconservative systems – ; combined fractional derivatives – ; variational calculus
• 刊名：Fractional Calculus and Applied Analysis
• 出版年：2012
• 出版时间：September 2012
• 年：2012
• 卷：15
• 期：3
• 页码：407-417
• 全文大小：178.5 KB
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• 作者单位：1. Faculty of Computer Science, Bia艂ystok University of Technology, 15-351 Bia艂ystok, Poland2. Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

文摘

A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional derivatives. The obtained results provide tools to carry out the quantization of nonconservative problems through combined fractional canonical equations of Hamilton type.