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

Solution of linear PDEs obtained using Laplace transform

“…Related applied research has been conducted on the Laplace transform and its generalized form. As an example of related applied research, immersed coupled fractional models in spheres and oscillatory pendulums were investigated [6], Laplace-based methods in linearized dynamical models in the presence of a Hilfer fractional operator were studied [7], and general solutions of ODEs related to Chebyshev polynomials of the second kind were also studied [8].…”

Closed-form asymptotic solution for the transport of chlorine concentration in composite pipes

“…Besides, the literature is heavily rich with various analytical and semi-analytical methods, which indeed pave the way for the acquisition of exact and closed-form solutions for subsequent use in computational methods as benchmark solutions. To mention a few, we recall the following methods that are widely used to analytically tackle a wide class of differential equations, including the numerical Laplace transform method [11], a mixture of Laplace transform and binomial expansion method for the solution coupled dynamical models [12], the generalized Laplace transform [13], the decomposition method by Adomian [14], the application improved decomposition technique for complex-valued evolution methods [15], generalized Hankel transform method [16], the Laplace-Fourier-sine transform method [17], the Wiener-Hopf method [18], the eigen-value approach [19], and the Lie's symmetry method [20] to state but just a few. In the same vein, it will be soothing to recall some of the reliable numerical methods that play a part in fluid flow problems.…”