Dissertation (MSc Mathematics)This research presents the existence and uniqueness of a solution to nonlocal problem for a loaded parabolic equation. The nonlocal condition of first kind is expressed to its equivalent nonlocal condition of second kind, which is necessary for qualitative study about the solvability of the problem. The theoretical analysis of study on existence and uniqueness of a generalized solution to a nonlocal problem is studied using Galerkin method, apriori method to obtain the approximate size of solution, numbers of inequalities and Gronwall’s lemma. The numerical approximation of the problem is obtained by using homotopy analysis method, where the initial base function is determined by using initial condition.