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Akbulut, Arzu; Islam, S. M. Rayhanul

Study on the Biswas-Arshed equation with the beta time derivative. (English) Zbl 1492.35406

Int. J. Appl. Comput. Math. 8, No. 4, Paper No. 167, 13 p. (2022).

Cited in 2 Documents

MSC:

35R11 Fractional partial differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35C05 Solutions to PDEs in closed form

Keywords:

Biswas-Arshed equation; improved \(F\)-expansion method; modified extended auxiliary equation mapping method; beta derivative
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Full Text: DOI

References:

[1] Hashemi, MS; Inc, M.; Yusuf, A., On three-dimensional variable order time fractional chaotic system with nonsingular kernel, Chaos Solitons Fractals, 133 (2020) · Zbl 1483.65117 · doi:10.1016/j.chaos.2020.109628
[2] Hashemi, MS; Akgül, A., Solitary wave solutions of time-space nonlinear fractional Schrödinger’s equation: two analytical approaches, J. Comput. Appl. Math., 339, 147-160 (2018) · Zbl 1392.35286 · doi:10.1016/j.cam.2017.11.013
[3] Darvishi, MT; Najafi, M.; Wazwaz, AM, Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions, Chaos Solitons Fractals, 150 (2021) · Zbl 1498.35568 · doi:10.1016/j.chaos.2021.111187
[4] Sadri, K., Hosseini, K., Baleanu, D., Ahmadian, A., Salahshour, S.: Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel. Adv. Difference Equations 348 (2021). · Zbl 1494.65104
[5] Hosseini, K.; Ilie, M.; Mirzazadeh, M.; Yusuf, A.; Sulaiman, TA; Baleanu, D.; Salahshour, S., An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense, Math. Comput. Simul., 187, 248-260 (2021) · Zbl 1540.76171 · doi:10.1016/j.matcom.2021.02.021
[6] Kaplan, M.; Akbulut, A., The analysis of the soliton type solutions of conformable equations by using generalized Kudryashov method, Opt. Quant. Electron., 53, 498 (2021) · doi:10.1007/s11082-021-03144-y
[7] Islam, SMR; Bashar, MH; Mohammad, N., Immeasurable soliton solutions and enhanced (G’/G)-expansion method, Physics Open, 9 (2021) · doi:10.1016/j.physo.2021.100086
[8] Bashar, MH; Islam, SMR; Kumar, D., Construction of traveling wave solutions of the (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation, Partial Differ. Equ. Appl. Math., 4 (2021) · doi:10.1016/j.padiff.2021.100040
[9] Yu, W.; Zhou, Q.; Mirzazadeh, M.; Liu, W.; Biswas, A., Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics, J. Adv. Res., 15, 69-76 (2019) · doi:10.1016/j.jare.2018.09.001
[10] Liu, W.; Zhang, Y.; Triki, H.; Mirzazadeh, M.; Ekici, M.; Zhou, Q.; Biswas, A.; Belic, M., Interaction properties of solitonics in inhomogeneous optical fibers, Nonlinear Dyn., 95, 557-563 (2019) · doi:10.1007/s11071-018-4582-6
[11] Hosseini, K.; Matinfar, M.; Mirzazadeh, M., Soliton solutions of high-order nonlinear Schrödinger equations with different laws of nonlinearities, Regul. Chaotic Dyn., 26, 1, 105-112 (2021) · Zbl 1473.35506 · doi:10.1134/S1560354721010068
[12] Podlubny, I., Fractional differential equations (1999), USA: Academic Press, USA · Zbl 0924.34008
[13] Atangana, A., Noutchie, S.C.O.: Model of Break-Bone Fever via Beta-Derivatives. BioMed Res. Int. 523159 (2014).
[14] Hussain, A.; Jhangeer, A.; Tahir, S.; Chu, YM; Khan, I.; Nisar, KS, Dynamical behavior of fractional Chen-Lee-Liu equation in optical fibers with beta derivatives, Results Phys., 18 (2020) · doi:10.1016/j.rinp.2020.103208
[15] Yıldırım, Y., Optical solitons of Biswas-Arshed equation in birefringent fibers by trial equation technique, Optik, 182, 810-820 (2019) · doi:10.1016/j.ijleo.2019.01.085
[16] Yıldırım, Y., Optical solitons of Biswas-Arshed equation by modified simple equation technique, Optik, 182, 986-994 (2019) · doi:10.1016/j.ijleo.2019.01.106
[17] Aliyu, AI; Inc, M.; Yusuf, A.; Baleanu, D.; Bayram, M., Dark-bright optical soliton and conserved vectors to the Biswas-Arshed equation with third-order dispersions in the absence of self-phase modulation, Front. Phys., 7, 28 (2019) · doi:10.3389/fphy.2019.00028
[18] Tahir, M.; Awan, AU; Rehman, HU, Dark and singular optical solitons to the Biswas-Arshed model with Kerr and power law nonlinearity, Optik, 185, 777-783 (2019) · doi:10.1016/j.ijleo.2019.03.108
[19] Özkan, YS, On the exact solutions to Biswas-Arshed equation involving truncated M-fractional space-time derivative terms, Optik Int. J. Light Elect. Opt., 227 (2021) · doi:10.1016/j.ijleo.2020.166109
[20] Zafar, A.; Bekir, A.; Raheel, M.; Razzaq, W., Optical soliton solutions to Biswas-Arshed model with truncated M-fractional derivative, Optik Int. J. Light Elect. Opt., 222 (2020) · doi:10.1016/j.ijleo.2020.165355
[21] Hosseini, K.; Mirzazadeh, M.; Ilie, M.; Gómez-Aguilar, JF, Biswas-Arshed equation with the beta time derivative: Optical solitons and other solutions, Optik Int. J. Light Elect. Opt., 217 (2020) · doi:10.1016/j.ijleo.2020.164801
[22] Demiray, ST, New solutions of Biswas-Arshed equation with beta time derivative, Optik Int. J. Light Elect. Opt., 222 (2020) · doi:10.1016/j.ijleo.2020.165405
[23] Hoque, F.; Roshid, H., Optical soliton solutions of the Biswas-Arshed model by the tan θ/2 expansion approach, Phys. Scr., 95 (2020) · doi:10.1088/1402-4896/ab97ce
[24] Tripathy, A., Sahoo, S., Saha Ray, S., Abdou, M. A.: New optical soliton solutions of Biswas-Arshed model with Kerr law nonlinearity. Int. J. Modern Phys. B 35(26), 2150263 (2021). · Zbl 1490.81132
[25] Sabi’u, J., Rezazadeh, H., Tariq, H., Bekir, A.: Optical solitons for the two forms of Biswas-Arshed equation. Modern Phys. Lett. B 33(25) 1950308 (2019).
[26] Kudryashov, NA, Periodic and solitary waves of the Biswas-Arshed equation, Optik Int. J. Light Elect. Opt., 200 (2020) · doi:10.1016/j.ijleo.2019.163442
[27] Aouadi, S.; Bouzida, A.; Daoui, AK; Triki, H.; Zhou, Q.; Liu, S., W-shaped, bright and dark solitons of Biswas-Arshed equation, Optik Int. J. Light Elect. Opt., 182, 227-232 (2019) · doi:10.1016/j.ijleo.2019.01.027
[28] Rehman, HU; Saleem, MS; Zubair, M.; Jafar, S., Optical solitons with Biswas-Arshed model using mapping method, Optik Int. J. Light Elect. Opt., 194 (2019) · doi:10.1016/j.ijleo.2019.163091
[29] Akram, G.; Sarfraz, M., Multiple optical soliton solutions for CGL equation with Kerr law nonlinearity via extended modified auxiliary equation mapping method, Optik Int. J. Light Elect. Opt., 242 (2021) · doi:10.1016/j.ijleo.2021.167258
[30] Seadawy, AR; Cheemaa, N.; Althobaiti, S.; Sayed, S.; Biswas, A., Optical soliton perturbation with fractional temporal evolution by extended modified auxiliary equation mapping, Rev. Mex. Fis., 67, 3, 403-414 (2021)
[31] Manafian, J.; İlhan, OA; Avazpour, L., The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs, Int. J. Nonlinear Sci. Numer. Simulation, 22, 1, 69-82 (2021) · Zbl 1525.35233 · doi:10.1515/ijnsns-2019-0279
[32] Akbar, MA; Ali, NHM, The improved F-expansion method with Riccati equation and its applications in mathematical physics, Cogent Math., 4, 1282577 (2017) · Zbl 1438.35344 · doi:10.1080/23311835.2017.1282577
[33] Islam, MS; Khan, K.; Akbar, MA; Mastroberardino, A., F-expansion method combined with Riccati equation applied to nonlinear evolution equations, Roy. Soc. Open Sci., 1 (2014) · doi:10.1098/rsos.140038
[34] Islam, MS; Akbar, MA; Khan, K., Analytical solutions of nonlinear Klein-Gordon equation using the improved F-expansion method, Opt. Quant. Electron., 50, 224 (2018) · doi:10.1007/s11082-018-1445-9
[35] Islam, MS; Akbar, MA; Khan, K., The improved F-expansion method and its application to the MEE circular rod equation and the ZKBBM equation, Cogent Math., 4, 1378530 (2017) · Zbl 1438.35356 · doi:10.1080/23311835.2017.1378530
[36] Mirzazadeh, M., Akbulut, A., Taşcan, F., Akinyemi, L.: A novel integration approach to study the perturbed Biswas-Milovic equation with Kudryashov’s law of refractive index. Optik Int. J. Light Elect. Opt. 252, 168529 (2022).
[37] Seadawy, AR; Cheemaa, N., Applications of extended modified auxiliary equation mapping method for high-order dispersive extended nonlinear Schrodinger equation in nonlinear optics, Mod. Phys. Lett. B, 18, 1950203 (2019) · doi:10.1142/S0217984919502038
[38] Seadawy, AR; Ali, A.; Raddadi, MH, Exact and solitary wave solutions of conformable time fractional Clannish Random Walker’s Parabolic and Ablowitz-Kaup-Newell-Segur equations via modified mathematical methods, Results Phys., 26 (2021) · doi:10.1016/j.rinp.2021.104374
[39] Akbar, M.A., Norhashidah, M. A.: The improved F-expansion method with Riccati equation and its applications in mathematical physics. Cogent Math., 2331-1835 (2017). · Zbl 1438.35344
[40] Islam, S.; Khan, K.; Akbar, MA, Application of the improved F -expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations, J. Egyptian Math. Soc., 25, 13-18 (2017) · Zbl 1357.35072 · doi:10.1016/j.joems.2016.03.008
[41] Bashar, MH; Islam, SMR, Exact solutions to the (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation by using modified simple equation and improve F-expansion methods, Phys. Open, 5 (2020) · doi:10.1016/j.physo.2020.100027
[42] Akbulut, A.; Hashemi, MS; Rezazadeh, H., New conservation laws and exact solutions of coupled Burgers’ equation, Waves Random Complex Media (2021) · doi:10.1080/17455030.2021.1979691
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