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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References
Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
Kilbas A, Srivastva HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. North-Holland mathematical studies. Elsevier Publications, p 204
Jingtang M, Liu J, Zhou Z (2014) Convergence analysis of moving finite element methods for space fractional differential equations. J Comput Appl Math 255:661–670
Gupta PK (2011) Approximate analytical solutions of fractional Benney-Lin equation by reduced differential transform method and the homotopy perturbation method. Comput Math Appl 58:2829–2842
Hammouch Z, Mekkaoui T (2013) Approximate analytical and numerical solutions to fractional KPP-like equations. Gen. Math Notes. 14(2):1–9
Hammouch Z, Mekkaoui T (2012) A Laplace-Variational Iteration method for solving the homogeneous Smoluchowski coagulation equation. Appl Math Sci 6(18):879–886
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. 334:30–40
Hariharan G (2009) Haar wavelet method for solving Cahn-Allen equation. Appl Math Sci 3:2523–2533
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):1951–1956
Tariq H, Akram G (2017) New travelling wave exact and approximate solutions for the nonlinear Cahn Allen equation: evolution of nonconserved quantity. Nonlinear Dyn 88:581–594
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
He JH (1999) Homotopy perturbation technique. Comput Methods Appl Mech Eng 178:257–262
Sakar MG, Uludag F, Erdogan F (2016) Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method. Appl Math Model 40:6639–6649
Prakash A, Kaur H (2017) Numerical solution for fractional model of Fokker-Planck equation by using q-HATM. Chaos Solitons Fractals 105:99–110
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
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Prakash, A., Kaur, H. (2021). An Efficient Numerical Technique for Solving the Time-Fractional Cahn–Allen Equation. In: Hura, G.S., Singh, A.K., Siong Hoe, L. (eds) Advances in Communication and Computational Technology. ICACCT 2019. Lecture Notes in Electrical Engineering, vol 668. Springer, Singapore. https://doi.org/10.1007/978-981-15-5341-7_3
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DOI: https://doi.org/10.1007/978-981-15-5341-7_3
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