Various perturbation methods
[1, 2] have been widely applied for obtaining approximate solutions of these equations, involving small parameter.
In the present work, we extend a homotopy perturbation method
with time-fractional derivatives to obtain solution for oxygen diffusion problem.
Here, we use alternative approach to solve (2) based on homotopy perturbation method
provides an expression for the desired solution in terms of a formal power series in a parameter that quantifies the deviation from the exactly solvable problem.
Application of iteration perturbation method
for nonlinear oscillators with discontinuities, Int.
Example include Yldrm and Momani  who applied the homotopy perturbation method
(HPM) to fractional oscillator and Koak and Yldrm  who solved the 3D Green's function by using HPM.
Cole, Multiple Scale and Singular Perturbation Methods
An additional advantage of higher-order perturbation methods
is that, like their first-order counterparts, they do not suffer from the curse of dimensionality.
An introduction on analysis, modeling, coupling methods and perturbation methods
Standard perturbation methods
provide a Taylor expansion of the policy functions that characterize the equilibrium of the economy in terms of the state variables of the model and a perturbation parameter.
While perturbation methods
guarantee that complete or exact disclosure (i.