Integral transformation for nonlinear oscillators

This paper introduces a generalized integral transform that encompasses the Laplace, Fourier, and numerous contemporary integral transforms as particular instances, while preserving their defining characteristics. Secondly, we propose the application of the generalized integral transform in the variational iteration method for the straightforward identification of the Lagrange multiplier, thus enabling the resolution of nonlinear oscillator problems. Finally, we present a series of illustrative examples to demonstrate the efficacy of this approach.