Abstract
Background: The dynamics of fractional oscillators are
generally described by fractional differential equations, which include the fractional
derivative of the Caputo or Riemann-Liouville type. These equations
induce classical oscillator equations like the harmonic oscillator equation, to
include fractional order derivatives. Solving fractional differential equations
numerically can be challenging due to the non-local nature of fractional derivatives.
Objective: In this paper, a recently developed integral Rohit transform is
utilized for solving systems of undamped and damped fractional oscillators characterized
by differential equations of fractional or non-integral order involving
the Caputo-fractional derivative operator. The solutions of fractional systems
which include undamped-simple fractional oscillators, undamped-driven fractional
oscillators, damped-driven fractional oscillators, and damped-fractional
oscillators are obtained. Methods: by applying the integral Rohit transform,
also written as RT. Differential equations of fractional or non-integral order
are generally solved by utilizing methods which include the fractional variational
iteration approach, the homotopy-perturbation method, the equivalent
linearized method, the Adomian decomposition method, etc. Results: This
paper demonstrates the effectiveness, reliability, and efficiency of the integral
Rohit transform in solving fractional systems, which include undamped-simple
fractional oscillators, undamped-driven fractional oscillators, damped-driven
fractional oscillators, and damped-fractional oscillators and are characterized
by differential equations of fractional or non-integral order involving the
Caputo-fractional derivative operator. Conclusions: The Rohit transform
brought the progressive principles or methodologies that offer new insights or
views on the problems examined in the paper, distinguishing itself from existing
methods and doubtlessly beginning up new research instructions. It provided
precise results for the specific problems discussed in the paper, surpassing the
capabilities of other methods in terms of decision, constancy, or robustness to
noise and disturbances.
generally described by fractional differential equations, which include the fractional
derivative of the Caputo or Riemann-Liouville type. These equations
induce classical oscillator equations like the harmonic oscillator equation, to
include fractional order derivatives. Solving fractional differential equations
numerically can be challenging due to the non-local nature of fractional derivatives.
Objective: In this paper, a recently developed integral Rohit transform is
utilized for solving systems of undamped and damped fractional oscillators characterized
by differential equations of fractional or non-integral order involving
the Caputo-fractional derivative operator. The solutions of fractional systems
which include undamped-simple fractional oscillators, undamped-driven fractional
oscillators, damped-driven fractional oscillators, and damped-fractional
oscillators are obtained. Methods: by applying the integral Rohit transform,
also written as RT. Differential equations of fractional or non-integral order
are generally solved by utilizing methods which include the fractional variational
iteration approach, the homotopy-perturbation method, the equivalent
linearized method, the Adomian decomposition method, etc. Results: This
paper demonstrates the effectiveness, reliability, and efficiency of the integral
Rohit transform in solving fractional systems, which include undamped-simple
fractional oscillators, undamped-driven fractional oscillators, damped-driven
fractional oscillators, and damped-fractional oscillators and are characterized
by differential equations of fractional or non-integral order involving the
Caputo-fractional derivative operator. Conclusions: The Rohit transform
brought the progressive principles or methodologies that offer new insights or
views on the problems examined in the paper, distinguishing itself from existing
methods and doubtlessly beginning up new research instructions. It provided
precise results for the specific problems discussed in the paper, surpassing the
capabilities of other methods in terms of decision, constancy, or robustness to
noise and disturbances.
Keywords
Rohit transform; Fractional oscillators; Capu
Keywords
Rohit transform; Fractional oscillators; Capu