Analytical investigation of the coupled fractional models for immersed spheres and oscillatory pendulums

In this research, coupled fractional models for immersed spheres and oscillatory pendulums have been proposed. We deploy the Laplace transform method together with the negative binomial formula to analytically investigate the dynamics of the systems. Approximate closed-form solutions are successfully revealed with the help of the convolution theorem. Additionally, we graphically illustrate the variational effects of the fractional-orders and the coupling parameters on the paired fields.

Automated summary

In this research, coupled fractional models for immersed spheres and oscillatory pendulums have been proposed. The dynamics of the systems are analytically investigated using the Laplace transform method and the negative binomial formula. The approximate closed-form solutions are successfully revealed with the help of the convolution theorem. Moreover, the variational effects of the fractional-orders and the coupling parameters on the paired fields are graphically illustrated.