The application of the homotopy analysis method to solve linear and nonlinear fractional differential equations
Other Title(s)
طريقة تحليل الهوموتوبي لحل نظام من المعادلات التفاضلية الجزئية الكسرية
Dissertant
al-Bustanji, Jamal Muhammad Abd al-Hamid
Thesis advisor
Comitee Members
al-Jaradat, Umar Khalid
al-Khalid, Kamil Mustafa
al-Taani, Ali Ayid
University
Mutah University
Faculty
Faculty of Science
Department
Department of Mathematics and Statistics
University Country
Jordan
Degree
Master
Degree Date
2009
English Abstract
-This thesis presents a modification of the Homotopy Analysis method (HAM).
The new modification extends the application of this method to solve systems of fractional partial differential equations (PDEs) and the space fractional diffusion equation.
The HAM is applied to construct numerical solutions.
The fractional derivatives are described in the Caputo sense.
Results obtained using the scheme presented here are in good agreement with the analytical solutions and the numerical results obtained before.
Moreover, issues like the effect of varying the auxiliary parameter h, auxiliary function H(t) and the auxiliary linear operator L on the order of local error and convergence of the method has been discussed.
Also, we notice that the Adomian decomposition method (ADM) is special case of the homotopy analysis method, which Allan proved it see (Allan, 2007).
Main Subjects
No. of Pages
35
Table of Contents
Table of contents.
Abstract.
Chapter one : Introduction.
Chapter two : Fractional calculus and some numerical approximate methods.
Chapter three : Applications for systems of fractional partial differential equations.
Chapter four : Analytical solution for the space fractional diffusion equation by HAM.
References.
American Psychological Association (APA)
al-Bustanji, Jamal Muhammad Abd al-Hamid. (2009). The application of the homotopy analysis method to solve linear and nonlinear fractional differential equations. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-304644
Modern Language Association (MLA)
al-Bustanji, Jamal Muhammad Abd al-Hamid. The application of the homotopy analysis method to solve linear and nonlinear fractional differential equations. (Master's theses Theses and Dissertations Master). Mutah University. (2009).
https://search.emarefa.net/detail/BIM-304644
American Medical Association (AMA)
al-Bustanji, Jamal Muhammad Abd al-Hamid. (2009). The application of the homotopy analysis method to solve linear and nonlinear fractional differential equations. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-304644
Language
English
Data Type
Arab Theses
Record ID
BIM-304644
