eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 2020-09-27 8 1 6 12 10.12691/ijpdea-8-1-2 IJPDEA2020812 article Mousumi Datta mousumi.math@mbstu.ac.bd 1 Umme Habiba 1 Md. Babul Hossain 1 Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail, Bangladesh In this paper we apply a new method, named Elzaki Substitution Method to solve nonlinear homogeneous and nonhomogeneous partial differential equations with mixed partial derivatives, which is based on Elzaki Transform. The proposed method introduces also Adomian polynomials and the nonlinear terms can be handled by the use of this polynomials. The proposed method worked perfectly to find the exact solutions of partial equations with mixed partial derivatives without any need of linearization or discretization in comparison with other methods such as Method of Separation of Variables (MSV) and Variation Iteration Method (VIM). Some illustrative examples are given to demonstrate the applicability and efficiency of proposed method. http://pubs.sciepub.com/ijpdea/8/1/2/ijpdea-8-1-2.pdf Partial Differential Equations Exact Solution Mixed Partial Derivatives Elzaki Transform Elzaki Substitution Method Adomian polynomial