A new fractional mechanics based on fractional addition

• W. Sang Chung ^[1] ; H. Hassanabadi ^[3] ; E. Maghsoodi ^[2]
  1. [1] Gyeongsang National University

     Gyeongsang National University

     Corea del Sur

     
  2. [2] Lorestan University

     Lorestan University

     Irán

     
  3. [3] Shahrood University of Technology, Shahrood, Iran

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• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 67, Nº. 1, 2021, págs. 68-74
• Idioma: inglés
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• Resumen

  • In this paper, we introduce a new fractional derivative to define a new fractional velocity and a new fractional acceleration with the fractional space translation symmetry, which is given by fractional addition. We also construct the fractional version for Newton mechanics with fractional space translation symmetry in one dimension. We show the conservation of fractional energy and formulate the fractional Hamiltonian formalism for the fractional mechanics with fractional space translation symmetry. We exhibit some examples for the fractional mechanics with fractional space translation symmetry.