© 2013. M. A. Abdou, M. M. El–Kojok & S. A. Raad. This is a research/review paper, distributed under the terms of the Creative Commons Attribution-Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Global Journal of Science Frontier Research Mathematics and Decision Sciences Volume 13 Issue 3 Version 1.0 Year 2013 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896 Analytic and Numeric Solution of Linear Partial Differential Equation of Fractional Order By M. A. Abdou, M. M. El–Kojok & S. A. Raad Alexandria University, Egypt Abstract - The existence and uniqueness solution of the Cauchy problem are discussed and proved in a Banach space E due to Bielecki method and Picard method depending on the properties we expect a solution to possess. Moreover, some properties concerning the stability of solution are obtained. The product Nyström method is used as a numerical method to obtain a linear system of algebraic equations. Also, many important theorems related to the existence and uniqueness solution of the algebraic system are derived. Finally, an application is given and numerical results are obtained. Keywords : linear partial differential equation of fractional order, semigroup, linear algebraic system, product nyström method. GJSFR-F Classification : MSC 2010: 32W50 AnalyticandNumericSolutionofLinearPartialDifferentialEquationofFractionalOrder Strictly as per the compliance and regulations of :