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In this paper, we investigate the approximate solutions for the fractional fuzzy acoustic wave equations. We use the Laplace transform and an iterative technique with the fractional Atangana–Baleanu–Caputo operator to archive the series form results for the mains equations, and the expected outcomes of the suggested kinds were calculated. Finally, numerical examples are presented to show the usability of our major results. [ABSTRACT FROM AUTHOR]

This paper presents alternative representations to traditional calculus of the Euler-Lagrangian equations, in the alternative representations these equations contain fractional operators. In this work, we consider two problems, the Lagrangian of a Pais-Uhlenbeck oscillator and the Hamiltonian of a two-electric pendulum model where the fractional operators have a regular kernel. The Euler-Lagrange formalism was used to obtain the dynamic model based on the Caputo-Fabrizio operator and the new fractional operator based on the Mittag-Leffler function. The simulations showed the effectiveness of these two representations for different values of γ. [ABSTRACT FROM AUTHOR]