Abstract
The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.
Highlights
The tool of the fractional calculus started to be successfully applied in many fields of science and engineering
The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus
Motivated by the above mentioned results in differential geometry, we discuss in this paper the hidden symmetries corresponding to the fractional Killing vectors and KillingYano tensors on curved spaces deeply related to physical systems
Summary
The tool of the fractional calculus started to be successfully applied in many fields of science and engineering (see, e.g., [1– 12] and the references therein). The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. The Caputo differential operator of fractional calculus is defined as [1–8]
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