Higher-Order Geodesic Equations from Non-Local Lagrangians and Complex Backward-Forward Derivative Operators

Rami Ahmad El-Nabulsi 1
  • 1 Athens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671, Athens, Greece

Abstract

Starting with an extended complex backwardforward derivative operator in differential geometry which is motivated from non-local-in-time Lagrangian dynamics, higher-order geodesic equations are obtained within classical differential geometrical settings. We limit our analysis up to the 2nd-order derivative where some applications are discussed and a number of features are revealed accordingly.

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