# Series solutions of time-fractional PDEs by homotopy analysis method

Ishak Hashim, O. Abdulaziz, A. Saif

Research output: Contribution to journalArticle

11 Citations (Scopus)

### 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.

Original language English 686512 Differential Equations and Nonlinear Mechanics 2008 https://doi.org/10.1155/2008/686512 Published - 2008

### Fingerprint

Homotopy Analysis Method
Series Solution
Fractional Differential Equation
Partial differential equations
Fractional
Partial differential equation
Fractional Derivative
Variable Coefficients
Convergence Theorem
Derivatives
Demonstrate

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics
• Mechanics of Materials

### Cite this

Series solutions of time-fractional PDEs by homotopy analysis method. / Hashim, Ishak; Abdulaziz, O.; Saif, A.

In: Differential Equations and Nonlinear Mechanics, Vol. 2008, 686512, 2008.

Research output: Contribution to journalArticle

@article{ed8d5812a79e4f068665105f1e4e1dbe,
title = "Series solutions of time-fractional PDEs by homotopy analysis method",
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.",
author = "Ishak Hashim and O. Abdulaziz and A. Saif",
year = "2008",
doi = "10.1155/2008/686512",
language = "English",
volume = "2008",
journal = "Differential Equations and Nonlinear Mechanics",
issn = "1687-4099",
publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - Series solutions of time-fractional PDEs by homotopy analysis method

AU - Hashim, Ishak

AU - Abdulaziz, O.

AU - Saif, A.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=59849106542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59849106542&partnerID=8YFLogxK

U2 - 10.1155/2008/686512

DO - 10.1155/2008/686512

M3 - Article

AN - SCOPUS:59849106542

VL - 2008

JO - Differential Equations and Nonlinear Mechanics

JF - Differential Equations and Nonlinear Mechanics

SN - 1687-4099

M1 - 686512

ER -