© 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
AnalyticandNumericSolutionofLinearPartialDifferentialEquationofFractionalOrder
Strictly as per the compliance and regulations of :