Abstract
In this work, we investigate a nonlinear fractional order Lotka-Voltera prey-predator model. It is also worth mentioning that we develop some results about the existence of the solution through fixed point theory. After investigating the existence results, we also develop a suitable technique with the help of Laplace transform coupled with Adomain decomposition in order to obtain the approximate solutions for the underlying model. Here, it should be kept in mind that we study the proposed model subject to variable coefficients. The results obtained via the aforesaid techniques are illustrated graphically via Matlab-16 corresponding to different fractional order by taking two cases.