Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method. (28th January 2009)

• Record Type: Journal Article
• Authors: Abdulaziz, O.; Hashim, I.; Saif, A.
• Other Names: Liao Shijun Academic Editor.
• Is Part Of: Differential equations and nonlinear mechanics. Volume 2008(2008)
• Publication Date: 2009-01-28
• Subjects: Differential equations, Nonlinear -- Periodicals; Nonlinear mechanics -- Periodicals; Équations différentielles non linéaires; Mécanique non linéaire; Differential equations, Nonlinear; Nonlinear mechanics; Chaos Theory; Differential Equations; Periodicals; Electronic journals; 515.35
• DOI: 10.1155/2008/686512
• Languages: English
• ISSNs: 1687-4099

Abstract

Abstract : The homotopy analysis method (HAM) is applied to solve linear and nonlinear fractional partial differential equations (fPDEs). The fractional derivatives are described by Caputo's sense. Series solutions of the fPDEs are obtained. A convergence theorem for the series solution is also given. The test examples, which include a variable coefficient, inhomogeneous and hyperbolic-type equations, demonstrate the capability of HAM for nonlinear fPDEs.