Abstract
This paper studies the existence and uniqueness of solutions of a non local initial boundary value problem of a singular two dimensional nonlinear fractional order partial differential equation involving the Caputo fractional derivative by employing the functional analysis. We first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of obtaining the a priori bound relies on the construction of a suitable multiplicator. From the resulted a priori estimate, we can establish the solvability of the associated linear problem. Then, by applying an iterative process based on the obtained results for the associated linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the considered nonlinear problem.