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2021 | OriginalPaper | Chapter

An Efficient Numerical Technique for Solving the Time-Fractional Cahn–Allen Equation

Authors : Amit Prakash, Hardish Kaur

Published in: Advances in Communication and Computational Technology

Publisher: Springer Nature Singapore

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Abstract

In this paper, we investigate the time-fractional Cahn–Allen equation (CAE) with a novel homotopy-based numerical technique, namely homotopy perturbation transform technique in which homotopy perturbation method and Laplace transform (LT) are combined. In order to verify the reliability and accuracy of the proposed technique, the numerical results are also presented graphically.

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Literature
1.
Podlubny I (1999) Fractional differential equations. Academic Press, San DiegoMATH
2.
Kilbas A, Srivastva HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. North-Holland mathematical studies. Elsevier Publications, p 204
3.
Jingtang M, Liu J, Zhou Z (2014) Convergence analysis of moving finite element methods for space fractional differential equations. J Comput Appl Math 255:661–670MathSciNetCrossRefMATH
4.
Gupta PK (2011) Approximate analytical solutions of fractional Benney-Lin equation by reduced differential transform method and the homotopy perturbation method. Comput Math Appl 58:2829–2842MathSciNetCrossRefMATH
5.
Hammouch Z, Mekkaoui T (2013) Approximate analytical and numerical solutions to fractional KPP-like equations. Gen. Math Notes. 14(2):1–9MathSciNet
6.
Hammouch Z, Mekkaoui T (2012) A Laplace-Variational Iteration method for solving the homogeneous Smoluchowski coagulation equation. Appl Math Sci 6(18):879–886MathSciNetMATH
7.
Prakash A, Kumar M, Baleanu D (2018) A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform. Appl Math Comput. 334:30–40MathSciNetMATH
8.
Hariharan G (2009) Haar wavelet method for solving Cahn-Allen equation. Appl Math Sci 3:2523–2533MathSciNetMATH
9.
Esen A, Yagmurlu NM, Tasbozan O (2013) Approximate analytical solution to time-fractional damped Burger and Cahn-Allen equations. Appl Math Inf Sci 7(5):1951–1956MathSciNetCrossRef
10.
Tariq H, Akram G (2017) New travelling wave exact and approximate solutions for the nonlinear Cahn Allen equation: evolution of nonconserved quantity. Nonlinear Dyn 88:581–594CrossRefMATH
11.
Rawashdeh, MS (2017) A reliable method for the space-time fractional Burgers and time-fractional Cahn-Allen equations via the FRDTM. Adv Diff Equ 99
12.
13.
Sakar MG, Uludag F, Erdogan F (2016) Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method. Appl Math Model 40:6639–6649MathSciNetCrossRefMATH
14.
Prakash A, Kaur H (2017) Numerical solution for fractional model of Fokker-Planck equation by using q-HATM. Chaos Solitons Fractals 105:99–110MathSciNetCrossRefMATH
15.
Gomez-Aguilar JF, Yepez-Martinez H, Torres-Jimenez J, Cordova-Fraga T, Escobar-Jimenez RF, Olivares-Peregrino VH (2017) Homotopy perturbation transform method for nonliner differential equations involving to fractional operator with exponential kernel. Adv Differ Equ 68
Metadata
Title
An Efficient Numerical Technique for Solving the Time-Fractional Cahn–Allen Equation
Authors
Amit Prakash
Hardish Kaur
Copyright Year
2021
Publisher
Springer Nature Singapore
Book
Advances in Communication and Computational Technology

Print ISBN: 978-981-15-5340-0

Electronic ISBN: 978-981-15-5341-7

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-15-5341-7_3