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This paper aims to derive the equivalent power-form representation for the Toda oscillator, which describes the intensity fluctuations of Nd:YAG lasers. A two-scale dimension transform is introduced to study the transient fractal response of Toda oscillator. Numerical simulations indicate that for increasing values of the fractal exponent α , the frequency of the Toda oscillator increases. [ABSTRACT FROM AUTHOR]

In this paper, an equivalent power-form transformation method with a weighted function is applied for solving the one-dimensional fractal Bratu's boundary value equation. Numerical integration solutions obtained from the equivalent Bratu's equation as well as those from its approximate Taylor's series solution reveal that the proposed methodology yields highly accurate solutions. Therefore, it is believed that by applying the power-form transformation, various fractal differential equations in which two scales are needed because of the physical laws involved in modeling the observed phenomena, can be solved by treating the nonlinear terms as equivalent power-form terms. [ABSTRACT FROM AUTHOR]