Semi-analytical Investigation for the ψ-Caputo Fractional Relaxation-oscillation Equation Using the Decomposition Method (European Journal of Pure and Applied Mathematics, 2024)
The relaxation-oscillation differential equation serves as the fundamental model governing the description of relaxation-oscillation processes with notable applications in fluid flow and oscillation dynamics. The present study seeks the help of the unswerving Adomian Decomposition Method (ADM) to construct a generalized recurrent scheme for the relaxation-oscillation differential equation conferred with the ψ-Caputo fractional derivative. Moreover, fractional-order derivatives are known for unearthing the hidden features that the classical integer-order derivatives are decient in revealing. Thus, the outcomes acquired through this method when applied to certain ψ-Caputo fractional Cauchy problems prove to be precise and steadfast in contrast to those attained using previously studied methods for solving this equation.
Keywords: ψ-Caputo derivative; fractional relaxation-oscillation equation; Adomian decomposition method; semi-analytical method.