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Volume 5, Issue 2
Toward a New Algorithm for Nonlinear Fractional Differential Equations

Fadi Awawdeh & S. Abbasbandy

DOI: 10.4208/aamm.11-m1155

Adv. Appl. Math. Mech., 5 (2013), pp. 222-234.

Published online: 2013-05

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  • Abstract

This paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.

  • Keywords

Homotopy analysis method, Laplace transform, fractional differential equations.

  • AMS Subject Headings

34A08, 74G10, 35C10, 44A10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-222, author = {Awawdeh , Fadi and Abbasbandy , S.}, title = {Toward a New Algorithm for Nonlinear Fractional Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {2}, pages = {222--234}, abstract = {

This paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m1155}, url = {http://global-sci.org/intro/article_detail/aamm/67.html} }
TY - JOUR T1 - Toward a New Algorithm for Nonlinear Fractional Differential Equations AU - Awawdeh , Fadi AU - Abbasbandy , S. JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 222 EP - 234 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.11-m1155 UR - https://global-sci.org/intro/article_detail/aamm/67.html KW - Homotopy analysis method, Laplace transform, fractional differential equations. AB -

This paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.

Awawdeh , Fadi and Abbasbandy , S.. (2013). Toward a New Algorithm for Nonlinear Fractional Differential Equations. Advances in Applied Mathematics and Mechanics. 5 (2). 222-234. doi:10.4208/aamm.11-m1155
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