Homotopy analysis method for space‐time fractional differential equations

The motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM). The first space-time fractional differential equation is transformed into a space fractional differential equation or a time fractional differential equation before the HAM. Then the power series solution is constructed by the HAM. Finally, taking the illustrative examples into consideration we reach the conclusion that the HAM is applicable and powerful technique to construct the solution of space-time fractional differential equations.

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On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.11.003 ◽

2019 ◽

Vol 137 ◽

pp. 203-212 ◽

Cited By ~ 16

Author(s):

Zaid Odibat

Keyword(s):

Linear Operator ◽

Differential Equations ◽

Fractional Differential Equations ◽

Homotopy Analysis Method ◽

Initial Approximation ◽

Optimal Selection ◽

Analysis Method ◽

Homotopy Analysis ◽

Fractional Differential ◽

Selection Of

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On the Application of Homotopy Analysis Method to Fractional Differential Equations

Journal of The Faculty of Science and Technology ◽

10.52981/jfst.vi7.947 ◽

2021 ◽

pp. 1-18

Author(s):

Khalid Suliman Aboodh ◽

Abu baker Ahmed

Keyword(s):

Exact Solution ◽

Differential Equations ◽

Fractional Differential Equations ◽

Homotopy Analysis Method ◽

Fractional Derivatives ◽

Analysis Method ◽

Homotopy Analysis ◽

Convergence Control ◽

Fractional Differential ◽

Convergence Control Parameter

In this paper, an attempt has been made to obtain the solution of linear and nonlinear fractional differential equations by applying an analytic technique, namely the homotopy analysis method (HAM). The fractional derivatives are described by Caputo’s sense. By this method, the solution considered as the sum of an infinite series, which converges rapidly to exact solution with the help of the nonzero convergence control parameter ℏ. Some examples are given to show the efficiently and accurate of this method. The solutions obtained by this method has been compared with exact solution. Also our graphical represented of the solutions have been given by using MATLAB software.

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Toward a New Algorithm for Nonlinear Fractional Differential Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.11-m1155 ◽

2013 ◽

Vol 5 (2) ◽

pp. 222-234

Author(s):

Fadi Awawdeh ◽

S. Abbasbandy

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Homotopy Analysis Method ◽

Analytical Techniques ◽

Analytic Solutions ◽

Analysis Method ◽

Transform Method ◽

Nonlinear Fractional Differential Equations ◽

Homotopy Analysis ◽

Fractional Differential

AbstractThis 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.

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