Two numerical methods for solving conformable fractional KGE equation
*Ahmed AnberCorresponding authorah.anber@gmail.comDepartment of MathematicsFaculty of Mathematics and InformaticUniversity of Science and Technology of OranOran, 31000, Algeria0009-0004-9769-9467View full profile → , Zoubir Dahmanizzdahmani@yahoo.frLaboratory of LAMDA-ROUniversity of Blida 1Blida, Algeria0000-0003-4659-0723View full profile → , Mehmet Zeki Sarikayasarikayamz@gmail.comDepartment of MathematicsFaculty of Science and ArtsDüzce UniversityDüzce, TurkeyView full profile →
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- Received:
- 12 Jul 2023
- Published Online:
- 30 Sep 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1788
- Pages:
- 1361–1370
Abstract
Keywords
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References
[1] T. Abdeljawad: On conformable fractional calculus, J. Comput. Appl. Math. 279, 57-66 (2015).
[2] A. Anber, Z. Dahmani: The Homotopy Analysis Method for Solving Some Fractional Differential Equations, Journal of Interdisciplinary Mathematics, 17(3), 255-269 (2014).
[3] C. Baishya, R. Rangarajan: A New Application of (G’/G) -Expansion Method for Travelling Wave Solutions of Fractional PDEs, International Journal of Applied Engineering Research, 13(11), 9936-9942 (2018).
[4] M. Bezziou, Z. Dahmani: New integral operators for conformable fractional calculus with applications, Journal of Interdisciplinary Mathematics, 25:4, 927-940 (2022).
[5] M.S.H. Chowdhury, I. Hashim: Application of homotopy perturbation method to Klein-Gordon and sine-Gordon equations, Chaos, Solitons & Fractals, 39(4), 1928-1935 (2009).
[6] S.M. El-Sayed: The decomposition method for studying the Klein-Gordon equation, Chaos, Solitons & Fractals, 18(5), 1025-1030 (2003).
[7] H. Günerhan, M. Yigider, J. Manafian, O.A. Ilhan: Numerical solution of fractional order logistic equations via conformable fractional differential transform method, Journal of Interdisciplinary Mathematics, 24:5, 1207-1220 (2021).
[8] H. Jafari, H. Tajadodi, N. Kadkhoda, D. Baleanu: Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations, Abstract and Applied Analysis, 2013.
[9] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh: A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264(5), 65-70 (2014).
[10] S.J. Liao: The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis, Shanghai Jiao Tong University, (1992).
[11] S.J. Liao: On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147(2), 499-513 (2004).
[12] S.J. Liao: Beyond perturbation: Introduction to the homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, (2003).
[13] S.J. Liao: Notes on the homotopy analysis method: some def nitions and theorems, Communication in Nonlinear Science and Numerical Simulation, 14, 983-997 (2009).
[14] X. Li, M.L. Wang: The (G’/G) - expansion method and travelling wave solution for a higher - order nonlinear schrodinger equation, Appl Math Computation, 208, 440-445 (2009).
[15] X. Li, Kamran, A. Ul Haq, X. Zhang: Numerical solution of the linear time fractional Klein-Gordon equation using transform based localized RBF method and quadrature, AIMS Mathematics, 5(5), 5287-5308 (2020).
[16] N. Raza, A.R. Butt, A. Javid: Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients, Journal of Function Spaces, 2016.
[17] A.S.V. Ravi Kanth, K. Aruna: Diffrential transform method for solving the linear and nonlinear Klein-Gordon equation, Computer Physics Communications, 180(5), 708-711 (2009).
[18] M. Songa, Y. Ge: Application of the (G’/G) -expansion method to (3+1)-dimensional nonlinear evolution equations, Computers and Mathematics with Applications, 60, 220-1227 (2010).
[19] M. Topsakal, F. Tascan: Exact Travelling Wave Solutions for Space-Time Fractional Klein-Gordon Equation and (2+1)-Dimensional Time-Fractional Zoomeron Equation via Auxiliary Equation Method, Applied Mathematics and Nonlinear Sciences, 5(1), 437-446 (2020).
[20] M.L. Wang, X. Li , J. Zhang: The (G’/G) - expansion method and evolution equations in mathematical physics, Phys. Lett. A, 372, 417-421 (2008).
[21] A.M. Wazwaz: The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein Gordon equation, Applied Mathematics and Computation, 167(2), 1179-1195 (2005).
[22] A.M. Yang, Y.Z. Zhang, C. Cattani, G.N. Xie, M.M. Rashidi, Y.J. Zhou, X.J. Yang: Application of Local Fractional Series E xpansion Method to Solve Klein-Gordon Equations on Cantor Sets, Abstract and Applied Analysis, 2014.
[23] E.Yusufoglu: The variational iteration method for studying th Klein-Gordon equation, Applied Mathematics Letters, 21(7), 669-674 (2008).
[24] E.M.E. Zayed: The (G’/G) -Expansion method and its application to some nonlinear evolution equations, J Appl Math Comput, 30, 89-103 (2009).
