Abstract
One-parameter Darboux deformations are established for the simple ordinary differential equation (ODE) satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (noninteger) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov–Lewis invariants for these sequences are also discussed.
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