Research Article
Year 2024,
Issue: 46, 71 - 88, 29.03.2024
Abstract
Project Number
HDP23F2
References
- S. A. Khuri, A. M. Wazwaz, Optical solitons and traveling wave solutions to Kudryashov’s equation, Optik 279 (2023) 170741 1-8.
- L. Akinyemi, M. Şenol, O. S. Iyiola, Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method, Mathematics and Computers in Simulation 182 (2021) 211-233.
- S. Yasin, A. Khan, S. Ahmad, M. S. Osman, New exact solutions of $(3+1)$-dimensional modified KdV-Zakharov-Kuznetsov equation by Sardar-subequation method, Optical and Quantum Electronics 56 (1) (2024) 90 1-15.
- S. Liu, Z. Fu, S. Liu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Physics Letters A 289 (1-2) (2001) 69-74.
- K. S. Nisar, O. A. Ilhan, S. T. Abdulazeez, J. Manafian, S. A. Mohammed, M. S. Osman, Novel multiple soliton solutions for some nonlinear PDEs via multiple exp-function method, Results in Physics 21 (2021) 103769 1-11.
- D. Kumar, J. Manafian, F. Hawlader, A. Ranjbaran, New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method, Optik 160 (2018) 159-167.
- M. M. Kabir, A. Khajeh, E. Abdi Aghdam, A. Yousefi Koma, Modified Kudryashov method for finding exact solitary wave solutions of higher‐order nonlinear equations, Mathematical Methods in the Applied Sciences 34 (2) (2011) 213-219.
- T. Aktürk, Modified exponential function method for nonlinear mathematical models with Atangana conformable derivative, Revista Mexicana de Física 67 (4) (2021) 1-18.
- E. M. E. Zayed, K. A. Gepreel, Some applications of the $(G'/G)$-expansion method to nonlinear partial differential equations, Applied Mathematics and Computations 212 (1) (2009) 1-13.
- X. Hu, M. Arshad, L. Xiao, N. Nasreen, A. Sarwar, Bright-dark and multi wave novel solitons structures of Kaup-Newell Schrödinger equations and their applications, Alexandria Engineering Journal 60 (4) (2021) 3621-3630.
- M. Nadeem, L. F. Iambor, The traveling wave solutions to a variant of the Boussinesq equation, Electronic Journal of Applied Mathematics 1 (3) (2023) 26-37.
- K. J. Wang, J. Si, Diverse optical solitons to the complex Ginzburg–Landau equation with Kerr law nonlinearity in the nonlinear optical fiber, The European Physical Journal Plus 138 (187) (2023) 1-15.
- A. Kumar, S. Kumar, S. P. Yan, Residual power series method for fractional diffusion equations, Fundamenta Informaticae 151 (1-4) (2017) 213-230.
- S. Liao, On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation 147 (2) (2004) 499-513.
- D. D. Ganji, A. Sadighi, Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Computational and Applied Mathematics 207 (1) (2007) 24-34.
- M. Gencyigit, M. Şenol, M. E. Koksal, Analytical solutions of the fractional $(3+1)$-dimensional Boiti-Leon-Manna-Pempinelli equation, Computational Methods for Differential Equations 11 (3) (2023) 564-575.
- N. Kadkhoda, H. Jafari, Analytical solutions of the Gerdjikov–Ivanov equation by using exp $(\phi(\xi))$-expansion method, Optik 139 (2017) 72-76.
- R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivatives, The Journal of Physical Chemistry B 104 (16) (2000) 3914-3917.
- L. Akinyemi, P. Veeresha, M. Şenol, H. Rezazadeh, An efficient technique for generalized conformable Pochhammer–Chree models of longitudinal wave propagation of elastic rod, Indian Journal of Physics 96 (14) (2022) 4209-4218.
- K. S. Nisar, L. Akinyemi, M. Inc, M. Şenol, M. Mirzazadeh, A. Houwe, H. Rezazadeh, New perturbed conformable Boussinesq-like equation: Soliton and other solutions, Results in Physics 33 (2022) 105200 1-10.
- B. Mohan, S. Kumar, R. Kumar, Higher-order rogue waves and dispersive solitons of a novel P-type(3+ 1)-D evolution equation in soliton theory and nonlinear waves, Nonlinear Dynamics 111 (21) (2023) 20275-20288.
- M. Mirzazadeh, L. Akinyemi, M. Şenol, K. Hosseini, A variety of solitons to the sixth-order dispersive $(3+1)$-dimensional nonlinear time-fractional Schrödinger equation with cubic-quintic-septic nonlinearities, Optik 241 (2021) 166318 1-15.
- Y. Çenesiz, A. Kurt, New fractional complex transform for conformable fractional partial differential equations, Journal of Applied Mathematics, Statistics and Informatics 12 (2) (2016) 41-47.
- R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264 (2014) 65-70.
- M. Şenol, M. Gençyiğit, M. E. Koksal, S. Qureshi, New analytical and numerical solutions to the(2+1)-dimensional conformable cpKP–BKP equation arising in fluid dynamics, plasma physics, and nonlinear optics, Optical and Quantum Electronics 56 (352) (2024) 1-18.
- M. A. Abdou, A. A. Soliman, Modified extended tanh-function method and its application on nonlinear physical equations, Physics Letters A 353 (6) (2006) 487-492.
- M. H. Ali, H. M. El-Owaidy, H. M. Ahmed, A. A. El-Deeb, I. Samir, Optical solitons for fourth-order nonlinear Schrödinger's equation with cubic–quintic–septic–nonic nonlinearity using improved modified extended tanh-function scheme, Ain Shams Engineering Journal 15 (2024) 102413 1-7}
- J. Ahmad, Z. Mustafa, J. Habib, Analyzing dispersive optical solitons in nonlinear models using an analytical technique and its applications, Optical and Quantum Electronics 56 (77) (2024) 1-20.
- K. Hosseini, A. Bekir, R. Ansari, Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the $\exp(–\phi(\xi))$-expansion method, Optical and Quantum Electronics 49 (2017) 1-11.
- M. Şenol, M. Gençyiğit, S. Sarwar, Different solutions to the conformable generalized $(3+1)$-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation arising in shallow-water waves, International Journal of Geometric Methods in Modern Physics 2023 (2023) 2350154 1-22.
- M. Alquran, Analytical solutions of fractional foam drainage equation by residual power series method, Mathematical Sciences 8 (4) (2014) 153-160.
- M. Şenol, M. Gençyiğit, A. Houwe, Analytical and numerical simulation of the conformable new extended(2+1)-dimensional Kadomtsev–Petviashvili equation, Numerical Heat Transfer, Part B: Fundamentals 2023 (2023) 1-17.
- M. N. Rafiq, H. Chen, Dynamics of three-wave solitons and other localized wave solutions to a new generalized(3+ 1)-dimensional p-type equation, Chaos, Solitons and Fractals 180 (2024) 1-10.
New Conformable P-Type $(3+1)$-Dimensional Evolution Equation and its Analytical and Numerical Solutions
Abstract
The paper examines the conformable nonlinear evolution equation in $(3+1)$-dimensions. First, basic definitions and characteristics for the conformable derivative are given. Then, the modified extended tanh-function and $\exp(–\phi(\xi))$-expansion techniques are utilized to determine the exact solutions to this problem. The consequences of some of the acquired data's physical 3D and 2D contour surfaces are used to demonstrate the findings, providing insight into how geometric patterns are physically interpreted. These solutions help illustrate how the studied model and other nonlinear representations in physical sciences might be used in real-world scenarios. It is clear that these methods have the capacity to solve a large number of fractional differential equations with beneficial outcomes.
Keywords
$(3+1)$-dimensional evolution equation modified extended tanh-function method $\exp(–\phi(\xi))$-expansion method residual power series method conformable derivative
Ethical Statement
All authors declare no conflict of interest.
Supporting Institution
Nevşehir Hacı Bektaş Veli University.
Project Number
HDP23F2
Thanks
NEVÜBAP
References
- S. A. Khuri, A. M. Wazwaz, Optical solitons and traveling wave solutions to Kudryashov’s equation, Optik 279 (2023) 170741 1-8.
- L. Akinyemi, M. Şenol, O. S. Iyiola, Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method, Mathematics and Computers in Simulation 182 (2021) 211-233.
- S. Yasin, A. Khan, S. Ahmad, M. S. Osman, New exact solutions of $(3+1)$-dimensional modified KdV-Zakharov-Kuznetsov equation by Sardar-subequation method, Optical and Quantum Electronics 56 (1) (2024) 90 1-15.
- S. Liu, Z. Fu, S. Liu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Physics Letters A 289 (1-2) (2001) 69-74.
- K. S. Nisar, O. A. Ilhan, S. T. Abdulazeez, J. Manafian, S. A. Mohammed, M. S. Osman, Novel multiple soliton solutions for some nonlinear PDEs via multiple exp-function method, Results in Physics 21 (2021) 103769 1-11.
- D. Kumar, J. Manafian, F. Hawlader, A. Ranjbaran, New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method, Optik 160 (2018) 159-167.
- M. M. Kabir, A. Khajeh, E. Abdi Aghdam, A. Yousefi Koma, Modified Kudryashov method for finding exact solitary wave solutions of higher‐order nonlinear equations, Mathematical Methods in the Applied Sciences 34 (2) (2011) 213-219.
- T. Aktürk, Modified exponential function method for nonlinear mathematical models with Atangana conformable derivative, Revista Mexicana de Física 67 (4) (2021) 1-18.
- E. M. E. Zayed, K. A. Gepreel, Some applications of the $(G'/G)$-expansion method to nonlinear partial differential equations, Applied Mathematics and Computations 212 (1) (2009) 1-13.
- X. Hu, M. Arshad, L. Xiao, N. Nasreen, A. Sarwar, Bright-dark and multi wave novel solitons structures of Kaup-Newell Schrödinger equations and their applications, Alexandria Engineering Journal 60 (4) (2021) 3621-3630.
- M. Nadeem, L. F. Iambor, The traveling wave solutions to a variant of the Boussinesq equation, Electronic Journal of Applied Mathematics 1 (3) (2023) 26-37.
- K. J. Wang, J. Si, Diverse optical solitons to the complex Ginzburg–Landau equation with Kerr law nonlinearity in the nonlinear optical fiber, The European Physical Journal Plus 138 (187) (2023) 1-15.
- A. Kumar, S. Kumar, S. P. Yan, Residual power series method for fractional diffusion equations, Fundamenta Informaticae 151 (1-4) (2017) 213-230.
- S. Liao, On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation 147 (2) (2004) 499-513.
- D. D. Ganji, A. Sadighi, Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Computational and Applied Mathematics 207 (1) (2007) 24-34.
- M. Gencyigit, M. Şenol, M. E. Koksal, Analytical solutions of the fractional $(3+1)$-dimensional Boiti-Leon-Manna-Pempinelli equation, Computational Methods for Differential Equations 11 (3) (2023) 564-575.
- N. Kadkhoda, H. Jafari, Analytical solutions of the Gerdjikov–Ivanov equation by using exp $(\phi(\xi))$-expansion method, Optik 139 (2017) 72-76.
- R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivatives, The Journal of Physical Chemistry B 104 (16) (2000) 3914-3917.
- L. Akinyemi, P. Veeresha, M. Şenol, H. Rezazadeh, An efficient technique for generalized conformable Pochhammer–Chree models of longitudinal wave propagation of elastic rod, Indian Journal of Physics 96 (14) (2022) 4209-4218.
- K. S. Nisar, L. Akinyemi, M. Inc, M. Şenol, M. Mirzazadeh, A. Houwe, H. Rezazadeh, New perturbed conformable Boussinesq-like equation: Soliton and other solutions, Results in Physics 33 (2022) 105200 1-10.
- B. Mohan, S. Kumar, R. Kumar, Higher-order rogue waves and dispersive solitons of a novel P-type(3+ 1)-D evolution equation in soliton theory and nonlinear waves, Nonlinear Dynamics 111 (21) (2023) 20275-20288.
- M. Mirzazadeh, L. Akinyemi, M. Şenol, K. Hosseini, A variety of solitons to the sixth-order dispersive $(3+1)$-dimensional nonlinear time-fractional Schrödinger equation with cubic-quintic-septic nonlinearities, Optik 241 (2021) 166318 1-15.
- Y. Çenesiz, A. Kurt, New fractional complex transform for conformable fractional partial differential equations, Journal of Applied Mathematics, Statistics and Informatics 12 (2) (2016) 41-47.
- R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264 (2014) 65-70.
- M. Şenol, M. Gençyiğit, M. E. Koksal, S. Qureshi, New analytical and numerical solutions to the(2+1)-dimensional conformable cpKP–BKP equation arising in fluid dynamics, plasma physics, and nonlinear optics, Optical and Quantum Electronics 56 (352) (2024) 1-18.
- M. A. Abdou, A. A. Soliman, Modified extended tanh-function method and its application on nonlinear physical equations, Physics Letters A 353 (6) (2006) 487-492.
- M. H. Ali, H. M. El-Owaidy, H. M. Ahmed, A. A. El-Deeb, I. Samir, Optical solitons for fourth-order nonlinear Schrödinger's equation with cubic–quintic–septic–nonic nonlinearity using improved modified extended tanh-function scheme, Ain Shams Engineering Journal 15 (2024) 102413 1-7}
- J. Ahmad, Z. Mustafa, J. Habib, Analyzing dispersive optical solitons in nonlinear models using an analytical technique and its applications, Optical and Quantum Electronics 56 (77) (2024) 1-20.
- K. Hosseini, A. Bekir, R. Ansari, Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the $\exp(–\phi(\xi))$-expansion method, Optical and Quantum Electronics 49 (2017) 1-11.
- M. Şenol, M. Gençyiğit, S. Sarwar, Different solutions to the conformable generalized $(3+1)$-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation arising in shallow-water waves, International Journal of Geometric Methods in Modern Physics 2023 (2023) 2350154 1-22.
- M. Alquran, Analytical solutions of fractional foam drainage equation by residual power series method, Mathematical Sciences 8 (4) (2014) 153-160.
- M. Şenol, M. Gençyiğit, A. Houwe, Analytical and numerical simulation of the conformable new extended(2+1)-dimensional Kadomtsev–Petviashvili equation, Numerical Heat Transfer, Part B: Fundamentals 2023 (2023) 1-17.
- M. N. Rafiq, H. Chen, Dynamics of three-wave solitons and other localized wave solutions to a new generalized(3+ 1)-dimensional p-type equation, Chaos, Solitons and Fractals 180 (2024) 1-10.
There are 33 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Methods and Special Functions |
| Journal Section | Research Article |
| Authors | |
| Project Number | HDP23F2 |
| Early Pub Date | March 28, 2024 |
| Publication Date | March 29, 2024 |
| Submission Date | January 15, 2024 |
| Acceptance Date | March 12, 2024 |
| Published in Issue | Year 2024 Issue: 46 |
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