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Zaman Konum Kesirli Liouville ve Sine-Gordon Denklemlerinin Yeni Dalga Çözümleri

Year 2018, , 295 - 303, 30.12.2018
https://doi.org/10.21597/jist.412948

Abstract

Bu makalede, yazarlar alt denklem yöntemi olarak adlandırılan güvenilir bir yöntem kullanarak zaman-uzay

kesirli Lioville ve Sine-Gordon denklemlerinin yeni dalga çözümlerini elde ettiler. Kullanılan denklemlerde mevcut

olan kesirli mertebeden türevler, conformable anlamında ele alınmıştır. Kolay, uıygulanabilir olan conformable

türevi, bilinen türevin sağladığı Leibniz Kuralı, bölüm kuralı, zincir kuralı gibi kuralları sağlar. Bu özellikler

conformable kesirli türeve diğer popüler türevler karşısında bir avantaj sağlamaktadır.

References

  • Abdeljawad T, (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279:57-66.
  • Cenesiz Y, Tasbozan O, Kurt A, (2017). Functional Variable Method for conformable fractional modifed KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10: 117-125.
  • Hashemi MS, 2018. Invariant subspaces admitted by fractional differential equations with conformable derivatives. Chaos, Solitons and Fractals, 107: 161-169.
  • Hosseini K, Manafian J, Samadani F, Foroutan M, Mirzazade, M, Zhou Q, (2017). Resonant Optical Solitons with Perturbation Terms and Fractional Temporal Evolution Using Improved tanh( (n) / 2)-Expansion Method and Exp Function Approach. Optik-International Journal for Light and Electron Optics, 158:933-939.
  • Ilie M, Biazar J, Ayati Z, (2018). The first integral method for solving some conformable fractional differential equations. Optical and Quantum Electronics, 50: 55.
  • Kaplan M, Ozer MN, (2018). Multiple-soliton solutions and analytical solutions to a nonlinear evolution equation. Optical and Quantum Electronics, 50:2.
  • Khalil R, Horani A, Yousef A, Sababheh M, 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264: 65-70.

New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations

Year 2018, , 295 - 303, 30.12.2018
https://doi.org/10.21597/jist.412948

Abstract

In this paper, the authors discussed the new wave solutions of time-space fractional Liouville and

Sine-Gordon equations by using a reliable analytical method called sub-equation method. The fractional derivatives

of considered equations are handled in conformable sense. Conformable derivative which is an easy and applicable

type of fractional derivative, satisfies basic properties of known derivative with integer order such as Leibniz

rule, quotient rule, chain rule. These properties of conformable derivative superior to other popular definitions on

obtaining analytical solutions of fractional equations.

References

  • Abdeljawad T, (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279:57-66.
  • Cenesiz Y, Tasbozan O, Kurt A, (2017). Functional Variable Method for conformable fractional modifed KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10: 117-125.
  • Hashemi MS, 2018. Invariant subspaces admitted by fractional differential equations with conformable derivatives. Chaos, Solitons and Fractals, 107: 161-169.
  • Hosseini K, Manafian J, Samadani F, Foroutan M, Mirzazade, M, Zhou Q, (2017). Resonant Optical Solitons with Perturbation Terms and Fractional Temporal Evolution Using Improved tanh( (n) / 2)-Expansion Method and Exp Function Approach. Optik-International Journal for Light and Electron Optics, 158:933-939.
  • Ilie M, Biazar J, Ayati Z, (2018). The first integral method for solving some conformable fractional differential equations. Optical and Quantum Electronics, 50: 55.
  • Kaplan M, Ozer MN, (2018). Multiple-soliton solutions and analytical solutions to a nonlinear evolution equation. Optical and Quantum Electronics, 50:2.
  • Khalil R, Horani A, Yousef A, Sababheh M, 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264: 65-70.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Orkun Taşbozan 0000-0001-5003-6341

Ali Kurt This is me 0000-0002-0617-6037

Publication Date December 30, 2018
Submission Date April 5, 2018
Acceptance Date July 26, 2018
Published in Issue Year 2018

Cite

APA Taşbozan, O., & Kurt, A. (2018). New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. Journal of the Institute of Science and Technology, 8(4), 295-303. https://doi.org/10.21597/jist.412948
AMA Taşbozan O, Kurt A. New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. J. Inst. Sci. and Tech. December 2018;8(4):295-303. doi:10.21597/jist.412948
Chicago Taşbozan, Orkun, and Ali Kurt. “New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations”. Journal of the Institute of Science and Technology 8, no. 4 (December 2018): 295-303. https://doi.org/10.21597/jist.412948.
EndNote Taşbozan O, Kurt A (December 1, 2018) New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. Journal of the Institute of Science and Technology 8 4 295–303.
IEEE O. Taşbozan and A. Kurt, “New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations”, J. Inst. Sci. and Tech., vol. 8, no. 4, pp. 295–303, 2018, doi: 10.21597/jist.412948.
ISNAD Taşbozan, Orkun - Kurt, Ali. “New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations”. Journal of the Institute of Science and Technology 8/4 (December 2018), 295-303. https://doi.org/10.21597/jist.412948.
JAMA Taşbozan O, Kurt A. New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. J. Inst. Sci. and Tech. 2018;8:295–303.
MLA Taşbozan, Orkun and Ali Kurt. “New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations”. Journal of the Institute of Science and Technology, vol. 8, no. 4, 2018, pp. 295-03, doi:10.21597/jist.412948.
Vancouver Taşbozan O, Kurt A. New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations. J. Inst. Sci. and Tech. 2018;8(4):295-303.