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Barikbin, Mohammad Saeed. (1402). Modified simple equation method (MSEM) for solving nonlinear (3+1)-dimensional space-time fractional equations. سامانه مدیریت نشریات علمی, 12(2), 413-424. doi: 10.22034/cmde.2023.51930.2168
Mohammad Saeed Barikbin. "Modified simple equation method (MSEM) for solving nonlinear (3+1)-dimensional space-time fractional equations". سامانه مدیریت نشریات علمی, 12, 2, 1402, 413-424. doi: 10.22034/cmde.2023.51930.2168
Barikbin, Mohammad Saeed. (1402). 'Modified simple equation method (MSEM) for solving nonlinear (3+1)-dimensional space-time fractional equations', سامانه مدیریت نشریات علمی, 12(2), pp. 413-424. doi: 10.22034/cmde.2023.51930.2168
Barikbin, Mohammad Saeed. Modified simple equation method (MSEM) for solving nonlinear (3+1)-dimensional space-time fractional equations. سامانه مدیریت نشریات علمی, 1402; 12(2): 413-424. doi: 10.22034/cmde.2023.51930.2168

Modified simple equation method (MSEM) for solving nonlinear (3+1)-dimensional space-time fractional equations

Computational Methods for Differential Equations
مقاله 15، دوره 12، شماره 2، خرداد 2024، صفحه 413-424    اصل مقاله (489.4 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.51930.2168
نویسنده
Mohammad Saeed Barikbin*
Department of Mathematics, Takestan branch, Islamic Azad University, Takestan, Iran
چکیده
In the present paper, modified simple equation method (MSEM) is implemented for obtaining exact solutions of three nonlinear (3 + 1)-dimensional space-time fractional equation, namely three types of modified Korteweg-de-Vries (mKdV) equations. Here, the derivatives are of the type of conformable fractional derivatives. The solving process produces a system of algebraic equations which is possible to be easily with no need of using software for determining unknown coefficients. Results show that this method can supply a powerful mathematical tool to construct exact solutions of mKdV equations and it can be employed for other nonlinear (3 + 1) - dimensional space-time fractional equations.
کلیدواژه‌ها
Modified simple equation method (MSEM)؛ Exact solutions؛ ( 3 + 1 )- Dimensional fractional equations؛ Conformable fractional derivative
مراجع
  • [1] P. Agarwal, S. Deniz,and S. Jain, AA. Alderremy ,and S. Aly., A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques, Physica A: Statistical Mechanics and its Applications, 15(542) (2020) , 122769.
  • [2] M. S. Ahmed, A. A. Zaghrout, and H. M. Ahmed, Travelling wave solutions for the doubly dispersive equation using improved modified extended tanh-function method, Alexandria Engineering Journal, 61(10) (2022), 7987– 7994.
  • [3] G. Akram, M. Sadaf, S. Arshed, and F. Sameen, Bright, dark, kink singular and periodic soliton solutions of Lakshmanan-Porsezian-Daniel model by generalized projective Riccati equations method, Optik, 241 (2021), 167051.
  • [4] G. Akram, M. Sadaf, and I. Zainab, The dynamical study of Biswas-Arshed equation via modified auxiliary equation method, Optik, 255 (2022), 168614.
  • [5] N. H. Aljahdaly and F. O. Al Zobidi, On the Schro¨dinger equation for deep water waves using the Pad´e-Adomian decomposition method, Journal of Ocean Engineering and Science, (2022).
  • [6] J. Biazar and Z. Ayati, Improved G’/G-expansion method and comparing with tanh-coth method, Applications and Applied Mathematics: An International Journal (AAM), 6(1) (2011), 20.
  • [7] N. Bildik and S. Deniz, A comparative study on solving fractional cubic isothermal autocatalytic chemical system via new efficient technique, Chaos, Solitons & Fractals, 132 (2020), 109555.
  • [8] E. Bonyah, A. K. Sagoe, D. Kumar, and S. Deniz, Fractional optimal control dynamics of coronavirus model with Mittag-Leffler law, Ecological Complexity, 45 (2021), 100880.
  • [9] J. L. Brent, E. N. Onder, and A. P. Andrew, Chapter 12 - Nonlinear differential equations, Advanced Mathematics for Engineering Students, Butterworth-Heinemann, (2022), 329–347.
  • [10] C. Chen, Singular solitons of Biswas-Arshed equation by the modified simple equation method, Optik, 184 (2019), 412–420.
  • [11] M. De la Sen, S. Deniz, and H. S¨ozen, A new efficient technique for solving modified Chua’s circuit model with a new fractional operator., Advances in Difference Equations, 1 (2021), 1–16.
  • [12] S. Deniz, A. Konuralp, and M. De la Sen, Optimal perturbation iteration method for solving fractional model of damped Burgers’ equation, Symmetry, 12(6) (2020), 958.
  • [13] S. Deniz and M. Sezer, Rational Chebyshev collocation method for solving nonlinear heat transfer equations, International Communications in Heat and Mass Transfer, 114 (2020), 104595.
  • [14] A. El Achab, Constructing of exact solutions to the nonlinear Schr¨odinger equation (NLSE) with power-law nonlinearity by the Weierstrass elliptic function method, Optik, 127(3) (2016), 1229–1232.
  • [15] E. M. Eskandari and N. Taghizadeh, Exact Solutions of Two Nonlinear Space-time Fractional Differential Equations by Application of Exp-function Method., Applications and Applied Mathematics: An International Journal (AAM), 15(2) (2020), 15.
  • [16] M. Eslami and M. Mirzazadeh, Exact solutions of modified Zakharov-Kuznetsov equation by the homogeneous balance method, Ain Shams Engineering Journal, 5(1) (2014), 221–225.
  • [17] O. Gonzalez-Gaxiola, A. Biswas, M. Ekici, and S. Khan, Highly dispersive optical solitons with quadratic-cubic law of refractive index by the variational iteration method, Journal of Optics, 51(1) (2022), 29–36.
  • [18] W. Hereman, R. Martino, J. Miller, L. Hong, S. Formenac, and A. Menz, Exact solutions of nonlinear partial differential equations The tanh/sech method, Math. Visiting Scholar Grant Program Wolfram Research Inc., Champaign, Illinois, 25 (2000), 1–26.
  • [19] R. Hirota, Exact envelope-soliton solutions of a nonlinear wave equation, Journal of Mathematical Physics, 14(7) (1973), 805–809.
  • [20] A. J. A. M. Jawad, M. D. Petkovi´c, and A. Biswas, Modified simple equation method for nonlinear evolution equations, Applied Mathematics and Computation, 217(2) (2010), 869–877.
  • [21] T. A. Khalil, N. Badra, H. M. Ahmed, and W. B. Rabie, Optical solitons and other solutions for coupled system of nonlinear Biswas-Milovic equation with Kudryashov’s law of refractive index by Jacobi elliptic function expansion method, Optik, (2022), 168540.
  • [22] R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of computational and applied mathematics, 264 (2014), 65–70.
  • [23] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, 204 (2006). elsevier.
  • [24] W. X. Ma, Soliton solutions by means of Hirota bilinear forms, Partial Differential Equations in Applied Mathematics, 5 (2022), 100220.
  • [25] S. K. Mohanty, S. Kumar, A. N. Dev, M. K. Deka, D. V. Churikov, and O. V. Kravchenko, An efficient technique of G0G-expansion method for modified KdV and Burgers equations with variable coefficients, Results in Physics, (2022), 105504.
  • [26] R. I. Nuruddeen, Multiple soliton solutions for the (3 + 1) conformable space-time fractional modified kortewegde-vries equations, Journal of Ocean Engineering and Science, 3(1) (2018), 11–18.
  • [27] H. M. Srivastava, S. Deniz, and K. M. Saad, An efficient semi-analytical method for solving the generalized regularized long wave equations with a new fractional derivative operator, Journal of King Saud University-Science, 33(2) (2021), 101345.
  • [28] N. Taghizadeh, M. Mirzazadeh, and F. Farahrooz, Exact soliton solutions for second-order Benjamin-Ono equation, Applications and Applied Mathematics: An International Journal (AAM), 6(1) (2011), 31.
  • [29] N. Taghizadeh, M. Mirzazadeh, AS. Paghaleh, and J. Vahidi, Exact solutions of nonlinear evolution equations by using the modified simple equation method, Ain Shams Engineering Journal, 3(3) (2012), 321–5.
  • [30] A. C. Varsoliwala and T. R. Singh, Mathematical modeling of atmospheric internal waves phenomenon and its solution by Elzaki Adomian decomposition method, Journal of Ocean Engineering and Science, 7(3) (2022), 203– 212.
  • [31] A. M. Wazwaz, Exact soliton and kink solutions for new (3+1)-dimensional nonlinear modified equations of wave propagation, Open Engineering, 7(1) (2017), 169–174.
  • [32] A. Zulfiqar and J. Ahmad, Soliton solutions of fractional modified unstable Schr¨odinger equation using Expfunction method, Results in Physics, 19 (2020), 103476.
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