ISSN 2347-1921 359 | Page Nov 16, 2013 G-function Solutions for Diffusion and Laplace's Equations Amir Pishkoo 1,2 , Maslina Darus 2 1 Physics Department, Nuclear Science Research School (NSTRI) P.O. Box 14395-836, Tehran, Iran apishkoo@gmail.com (corresponding author) 2 School of Mathematical Sciences, Faculty of Science and Technology UniversitiKebangsaan Malaysia, 43600 Bangi, Selangor Darul.Ehsan, Malaysia maslina@ukm.my ABSTRACT In this paper the Diffusion equation and Laplace's equation is solved by Modified separation of variables (MSV) method, suggested by Pishkoo and Darus. Using this method, Meijer's G-function solutions are derived in cylindrical coordinates system for two typical problems. These complex functions include all elementary functions and most of the special functions which are the solution of extensive problems in Physics and engineering. Keywords: Meijer's G-function; Partial differential equation; Modified separation of variables; Diffusion equation; Laplace's equation. Council for Innovative Research Peer Review Research Publishing System Journal: Journal of Advances in Mathematics Vol 4, No 1 editor@cirworld.com www.cirworld.com, member.cirworld.com