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New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

Loubna Ouahid

Physics Department, College of Science, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

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M. A. Abdou

Physics Department, College of Science, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt

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S. Owyed

Mathematics Department, College of Science, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

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, and

Sachin Kumar

https://orcid.org/0000-0003-4451-3206

Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, New Delhi 110007, Delhi NCT, India

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0217984921504443Cited by:22 (Source: Crossref)

Abstract

The deoxyribonucleic acid (DNA) dynamical equation, which emerges from the oscillator chain known as the Peyrard–Bishop (PB) model for abundant optical soliton solutions, is presented, along with a novel fractional derivative operator. The Kudryashov expansion method and the extended hyperbolic function (HF) method are used to construct novel abundant exact soliton solutions, including light, dark, and other special solutions that can be directly evaluated. These newly formed soliton solutions acquired here lead one to ask whether the analytical approach could be extended to deal with other nonlinear evolution equations with fractional space–time derivatives arising in engineering physics and nonlinear sciences. It is noted that the newly proposed methods’ performance is most reliable and efficient, and they will be used to construct new generalized expressions of exact closed-form solutions for any other NPDEs of fractional order.

Keywords:

References

1. A. Zafar, A. Bekir, M. Raheel and H. Rezazadeh, Int. J. Appl. Comput. Math. 6 (2020) 65. Crossref, Google Scholar
2. B. Ghanbari and J. F. Gómez-Aguilar, Mod. Phys. Lett. B 33(20) (2019) 1950235. Link, Web of Science, ADS, Google Scholar
3. B. Ghanbari and J. F. Gómez-Aguilar, Mod. Phys. Lett. B 33(32) (2019) 1950402. Link, Web of Science, ADS, Google Scholar
4. A. Biswas and R. T. Alqahtani, Optik 147 (2017) 72. Crossref, Web of Science, ADS, Google Scholar
5. H. Rezazadeh et al., Nonlinear Eng. 8(1) (2019) 224. Crossref, ADS, Google Scholar
6. J.-H. He, Results Phys. 17 (2020) 103031. Crossref, Web of Science, Google Scholar
7. Y. Yıldırım and M. Mirzazadeh, Chin. J. Phys. 64 (2020) 183. Crossref, Web of Science, Google Scholar
8. B. A. Malomed, D. Mihalache, F. Wise and L. Torner, J. Opt. B, Quantum Semiclass. Opt. 7(5) (2005) R53. Crossref, Google Scholar
9. M. A. Zafar and A. B. Raheel, Optik 204 (2020) 164133. Crossref, Web of Science, ADS, Google Scholar
10. M. A. Abdou, Indian J. Phys. 93(4) (2019) 537. Crossref, Web of Science, ADS, Google Scholar
11. M. A. Abdou, Waves Random Complex Media 30(2) (2020) 380. Crossref, Web of Science, ADS, Google Scholar
12. M. Abdou, S. Owyed, B. M. Raffah and S. Abdel-Khalek, Results Phys. 16 (2020) 102895. Crossref, Web of Science, Google Scholar
13. L. Ouahid, Phys. Scr. 96 (2021) 035224. Crossref, Web of Science, Google Scholar
14. S. Owyed, M. A. Abdou, A. Abdel-Aty and H. Dutta, AIMS Math. 5 (2020) 2057. Crossref, Web of Science, Google Scholar
15. A. A. Hendi, L. Ouahid, S. Owyed and M. A. Abdou, Results Phys. 24 (2021) 104152. Crossref, Web of Science, Google Scholar
16. M. A. Abdou, Int. J. Nonlinear Sci. 26 (2018) 55. Google Scholar
17. M. A. Abdou and A. Soliman, Results Phys. 9 (2018) 1497. Crossref, Web of Science, ADS, Google Scholar
18. M. A. Abdou, J. Ocean Eng. Sci. 2 (2017) 288. Crossref, Web of Science, Google Scholar
19. L. V. C. Hoan, S. Owyed, M. Inc, L. Ouahid, M. A. Abdou and Y.-M. Chu, Results Phys. 18 (2020) 103203. Crossref, Web of Science, Google Scholar
20. M. A. Abdou and A. Yildirim, Int. J. Numer. Methods Heat Fluid Flow 22 (2012) 829. Crossref, Web of Science, Google Scholar
21. M. A. Abdou and A. Elhanbaly, Nonlinear Sci. Lett. A 6 (2015) 10. Google Scholar
22. M. A. Abdou, A. Elhanbaly and M. T. Attia, Nonlinear Sci. Lett. A 7 (2016) 86. Google Scholar
23. M. A. Abdou, L. Ouahid, S. Owyed, A. M. Abdel-Baset, M. Inc, M. A. Akinlar and Y. M. Chu, AIMS Math. 5(6) (2020) 7272. Crossref, Web of Science, Google Scholar
24. M. A. Abdou, S. Owyed, S. Saha Ray, M. Inc, Y. M. Chu and L. Ouahid, Adv. Math. Phys. 2020 (2020) 8323148. Crossref, Web of Science, Google Scholar
25. M. Peyrard and A. R. Bishop, Phys. Rev. Lett. 62 (1989) 2755. Crossref, Web of Science, ADS, Google Scholar
26. J. Manafian, O. A. Ilhan and S. A. Mohammed, AIMS Math. 5(3) (2020) 2461. Crossref, Web of Science, Google Scholar
27. K. K. Ali, C. Cattani, J. F. Gómez-Aguilar, D. Baleanu and M. S. Osman, Chaos Solitons Fractals 139 (2020) 110089. Crossref, Web of Science, Google Scholar
28. K. R. Raslan, K. A. Khalid and M. A. Shallal, Chaos Solitons Fractals 103 (2017) 404. Crossref, Web of Science, ADS, Google Scholar
29. H. Yépez-Martínez, J. F. Gómez-Aguilar and D. Baleanu, Optik 155 (2018) 357. Crossref, Web of Science, ADS, Google Scholar
30. H. Yépez-Martínez and J. F. Gómez-Aguilar, Waves Random Complex Media 31(3) (2019) 573. Crossref, Web of Science, ADS, Google Scholar
31. H. Yépez-Martínez and J. F. Gómez-Aguilar, Waves Random Complex Media 29(4) (2019) 678. Crossref, Web of Science, ADS, Google Scholar
32. H. Yépez-Martínez, J. F. Gómez-Aguilar and A. Atangana, Math. Model. Nat. Phenom. 13(1) (2018) 14. Crossref, Web of Science, Google Scholar
33. H. M. Baskonus and J. F. Gómez-Aguilar, Mod. Phys. Lett. B 33(21) (2019) 1950251. Link, Web of Science, ADS, Google Scholar
34. H. Yépez-Martínez and J. F. Gómez-Aguilar, Opt. Quantum Electron. 50(10) (2018) 1. Crossref, Web of Science, Google Scholar
35. J. F. Gómez-Aguilar, Mod. Phys. Lett. B 33(26) (2019) 1950316. Link, Web of Science, ADS, Google Scholar
36. J. F. Gómez-Aguilar, Optik 168 (2018) 728. Crossref, Web of Science, ADS, Google Scholar
37. A. Yusuf, M. Inc, A. I. Aliyu and D. Baleanu, Front. Phys. 7 (2019) 34. Crossref, Web of Science, Google Scholar
38. M. F. Uddin, M. G. Hafez, Z. Hammouch and D. Baleanu, Waves Random Complex Media (2020). https://doi.org/10.1080/17455030.2020.1722331 Google Scholar
39. K. R. Raslan, S. E. Talaat and K. A. Khalid, Eur. Phys. J. Plus 132 (2017) 49. Crossref, Web of Science, Google Scholar
40. K. A. Khalid, R. I. Nuruddeen and K. R. Raslan, Opt. Quantum Electron. 50 (2018) 61. Crossref, Web of Science, Google Scholar
41. K. A. Khalid, R. I. Nuruddeen and K. R. Raslan, Chaos Solitons Fractals 106 (2018) 304. Crossref, Web of Science, Google Scholar
42. K. A. Khalid and R. I. Nuruddeen, Int. J. Phys. Res. 5(2) (2017) 109. Crossref, Google Scholar
43. V. F. Morales-Delgado, J. F. Gómez-Aguilar and M. A. Taneco-Hernandez, AEU — Int. J. Electron. Commun. 85 (2018) 108. Crossref, Web of Science, Google Scholar
44. A. Atangana and R. T. Alqahtani, Entropy 18 (2016) 40. Crossref, Web of Science, ADS, Google Scholar
45. M. Caputo and M. Fabrizio, Prog. Fract. Differ. Appl. 1(2) (2015) 73. Google Scholar
46. R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, J. Comput. Appl. Math. 264 (2014) 65. Crossref, Web of Science, Google Scholar
47. J. V. C. Sousa and E. C. Oliveira, Int. J. Anal. Appl. 16(1) (2018) 83. Web of Science, Google Scholar
48. B. Ghanbari and J. F. Gómez-Aguilar, Rev. Mex. Fís. 65 (2019) 503. Crossref, Web of Science, Google Scholar
49. H. Rezazadeh, S. M. Mirhosseini-Alizamini, M. Eslami, M. Rezazadeh, M. Mirzazadeh and S. Abbagari, Optik 172 (2018) 545. https://doi.org/10.1016/j.ijleo.2018.06.111 Crossref, Web of Science, ADS, Google Scholar
50. M. Inc, A. I. Aliyu, A. Yusuf and D. Baleanu, Mod. Phys. Lett. B 33 (2019) 1950224. https://doi.org/10.1142/S0217984919502233 Link, Web of Science, ADS, Google Scholar
51. M. Inc, A. I. Aliyu, A. Yusuf, D. Baleanu and M. Bayram, Front. Phys. 7 (2018) 28. https://doi.org/10.3389/fphy.2019.00028 Google Scholar
52. A. Atangana, D. Baleanu and A. Alsaedi, Open Phys. 14 (2016) 145. Crossref, Web of Science, Google Scholar
53. S. Zdravkovíc, J. Nonlinear Math. Phys. 18 (2001) 463. Link, Web of Science, ADS, Google Scholar
54. T. Dauxois, Phys. Lett. A 159 (1991) 390. Crossref, Web of Science, ADS, Google Scholar
55. M. A. Aguero, M. D. L. Najera and M. Carrillo, Int. J. Mod. Phys. B 22 (2008) 2571. Link, Web of Science, ADS, Google Scholar
56. L. Najera, M. Carrillo and M. A. Aguero, Adv. Stud. Theor. Phys. 4 (2010) 495. Google Scholar
57. S. Zdravkovíc, J. A. Tuszynski and M. V. Sataríc, J. Comput. Theor. Nanosci. 2 (2005) 1. Crossref, Google Scholar
58. S. Zdravkovíc and M. V. Sataríc, Phys. Lett. A 373 (2009) 2739. Crossref, Web of Science, ADS, Google Scholar
59. S. Kumar, A. Kumar and W. X. Ma, Chin. J. Phys. 69 (2021) 1. Crossref, Web of Science, ADS, Google Scholar
60. S. Sahoo, S. Saha Ray and M. A. Abdou, Alex. Eng. J. 59 (2020) 3105. Crossref, Web of Science, Google Scholar
61. L. Ouahid, S. Owyed, M. A. Abdou, N. A. Alshehri and S. K. Elegan, Alex. Eng. J. 60 (2021) 5495. Crossref, Web of Science, Google Scholar
62. S. Kumar and S. Rani, Pramana 95 (2021) 51. Crossref, Web of Science, ADS, Google Scholar
63. S. Kumar and M. Niwas, Mod. Phys. Lett. B 35(15) (2021) 2150252. Link, Web of Science, ADS, Google Scholar
64. S. Kumar and A. Kumar, Mod. Phys. Lett. B 34(01) (2020) 2150015. Link, Web of Science, ADS, Google Scholar

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Vol. 35, No. 26

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History

Received 2 June 2021

Accepted 8 July 2021

Published: 19 August 2021

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New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

Abstract

References

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New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

Abstract

References

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