Applications of Elzaki decomposition method to fractional relaxation-oscillation and fractional biological population equations

Elzaki decomposition method (EDM) is adopted to deal with the fractional-order relaxation and damped oscillation equation along with time-fractional spatial diffusion biological population model in different suitable habitat situations. In accordance with the graphs for the solutions obtained, the fractional relaxation exhibits super-slow phenomenon due to its extended descent, and fractional damped oscillation is an intermediate process that explains damped oscillation dynamic systems induced by some attenuated oscillations. The biological population model of time-fractional spatial diffusion depicts a rapid rise in population density in an ecosystem in a suitable habitat that is migrating from an unfavourable zone.