On the solution of fractional order partial differential equations with wavelet basis functions

Abstract

A vast application of partial differential equations in different physical and engineering sciences, and the main role that be playing by fractional differential equations to the best representation of various phenomena and real world problems therefore derived and developed a new numerical techniques is necessity. The aim of this thesis, is to introduce new wavelet technique based on the generalized Gegenbauer- Humbert polynomials; we call this method generalized Gegenbauer- Humbert wavelet. Utilized the proposed method to solve fractional differential equations (linear and non-linear) with initial and boundary- initial conditions. According to this new technique allows us to examine and select the best method to solve the problems under discussion; this method uni es some known wavelet methods in one formula. The proposed method established the ef ciency and accuracy when used to solve fractional differential equations (linear and non-linear) with ordinary, partial and coupled systems of fractional partial differential equations. The performance of our method is analyzed by comparing it with other different numerical methods; the convergence analysis is inspected in addition.