Analytical survey of the predator–prey model with fractional derivative order
Source abstract
Abstract
This work addresses the analytical investigation of the prey–predator behavior modeled by nonlinear evolution equation systems with fractional derivative order. Through the New Extended Algebraic Method (NEAM), we unearthed diverse types of soliton solutions including bright, dark solitons, combined trigonometric function solutions, and singular solutions. Besides the results obtained in the work of Khater, some new complex soliton solutions are also unearthed. The NEAM can also be used like the synthesis of the two mathematical tools.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nonlinear Waves and Solitons · Fractional Differential Equations Solutions · Advanced Differential Equations and Dynamical Systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Basic Science, Faculty of Mines and Petroleum Industries, University of Maroua 1 , P.O. Box 08, Káĺ, Cameroon
Department of Physics, Faculty of Science, The University of Maroua 2 , P.O. Box 814, Maroua, Cameroon
Department of Mathematics, Huzhou University 3 , Huzhou 313000, China
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology 4 , Changsha 410114, China
Department of Mathematics, Science Faculty, Firat University 5 , 23119 Elazig, Turkey
Department of Medical Research, China Medical University Hospital, China Medical University 6 , Taichung, Taiwan
Faculty of Engineering Technology, Amol University of Special Modern Technologies 7 , Amol, Iran
Department of Physics, Faculty of Science, The University of Ngaoundere 8 , P.O. Box 454, Ngaoundere, Cameroon
Funding
Foundation for Innovative Research Groups of the National Natural Science Foundation of China
References (51)
Show source-provided references
1. Two effective computational schemes for a prototype of an excitable system10.1063/5.0024417 ↗
2. London dispersion in molecular chemistry—Reconsidering steric effects10.1002/anie.201503476 ↗
3. The morphology of price dispersion10.1111/iere.12134 ↗
4. A Prey-Predator model with a reserved area10.15388/na.2007.12.4.14679 ↗
5. New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation10.1016/j.ijleo.2018.06.111 ↗
6. Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system10.1007/s11071-018-4198-x ↗
7. The discrete tanh method for solving the nonlinear differential-difference equations10.1142/s0217979220501775 ↗
8. Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics10.1515/phys-2020-0177 ↗
9. Solitary pulses of the conformable derivative nonlinear differential equation governing wave propagation in low-pass electrical transmission line10.1088/1402-4896/ab5055 ↗
10. Gray solitary-wave solutions in nonlinear negative-index materials10.1103/physreve.82.046603 ↗
11. Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations10.1103/PhysRevE.93.062202 ↗
12. Chirped soliton-like solutions of generalized nonlinear Schrödinger equation for pulse propagation in negative index material embedded into a Kerr medium10.1007/s12648-016-0840-y ↗
13. Chirped femtosecond solitons and double-kink solitons in the cubic-quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift10.1103/physreva.84.063830 ↗
14. Application of newly proposed sub-ODE method to locate chirped optical solutions to Triki-Biswas equation10.1016/j.ijleo.2020.164360 ↗
15. Rogue waves of the Fokas–Lenells equation10.1143/jpsj.81.124007 ↗
16. Optical solitons for higher-order nonlinear Schrödingers equation with three exotic integration architectures10.1016/j.ijleo.2018.11.027 ↗
17. Exact dipole solitary wave solution in metamaterials with higher-order dispersion10.1080/09500340.2016.1185178 ↗
18. Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: Application to negative index materials10.1103/physrevlett.95.013902 ↗
19. Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class10.1016/j.jksus.2018.08.013 ↗
20. Miscellaneous new traveling waves in metamaterials by means of the new extended direct algebraic method10.1016/j.ijleo.2019.163108 ↗
21. Soliton solutions in different classes for the Kaup-Newell model equation10.1142/s0217984920500384 ↗
22. Chirped solitons in negative index materials generated by Kerr nonlinearity10.1016/j.rinp.2020.103097 ↗
23. One method for finding exact solutions of nonlinear differential equations10.1016/j.cnsns.2011.10.016 ↗
24. DNA dynamics studied using the homogenous balance method10.1088/0256-307x/29/8/080203 ↗
25. Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations10.1016/j.rinp.2020.103127 ↗
26. Analytical and numerical solutions of the generalized dispersive Swift-Hohenberg equation10.1016/j.physleta.2013.01.007 ↗
27. Quasi-exact solutions of the dissipative Kuramoto-Sivashinsky equation10.1016/j.amc.2013.03.062 ↗
28. Exact solutions of the Kudryashov-Sinelshchikov equation using the multiple (G′/G)-expansion method10.1016/j.amc.2011.09.027 ↗
29. Chirped solitons in discrete electrical transmission line10.1016/j.rinp.2020.103188 ↗
30. The (G′/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics10.1016/j.physleta.2007.07.051 ↗
31. Analytic study on two nonlinear evolution equations by using the (G′/G)-expansion method10.1016/j.amc.2008.12.064 ↗
32. Exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form using two strategic integrations10.1140/epjp/s13360-020-00384-x ↗
33. Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group velocity dispersion regimes10.1103/physreva.93.023834 ↗
34. Diverse chirped optical solitons and new complex traveling waves in nonlinear optical fibers10.1088/1572-9494/ab7ecd ↗
35. New solitary waves for the Klein-Gordon-Zakharov equations10.1142/s0217984920502462 ↗
36. A series of abundant new optical solitons to the conformable space-time fractional perturbed nonlinear Schrodinger equation10.1088/1402-4896/ab9dad ↗
37. Exact optical solitons to the perturbed nonlinear equation with Schrödinger dual-power law of nonlinearity10.1007/s11082-020-02412-7 ↗
38. New exact solitary waves solutions to the fractional Fokas-Lenells equation via Atangana-Baleanu derivative operator10.1142/s0217979220503099 ↗
39. The propagation of waves in thin-film ferroelectric materials10.1007/s12043-019-1774-7 ↗
40. Scattering behavior of waveguide channels of a new coupled integrable dispersionless system10.1088/0256-307x/28/12/120501 ↗
41. Traveling wave-guide channels of a new coupled integrable dispersionless system10.1088/0253-6102/57/1/03 ↗
42. N-rotating loop-soliton solution of the coupled integrable dispersionless equation10.4236/jamp.2017.56113 ↗
43. Controllable rational solutions in nonlinear optics fibers10.1140/epjp/s13360-020-00640-0 ↗
44. The extended modified method applied to optical solitons solutions in birefringent fibers with weak nonlocal nonlinearity and four wave mixing10.1016/j.cjph.2019.02.002 ↗
45. Rogue wave dynamics in barotropic relaxing media10.1007/s12043-018-1633-y ↗
46. Reproducing kernel Hilbert space method for solving Bratu’s problem10.1007/s40840-014-0018-8 ↗
47. Improved (G′G)-expansion method for the space and time fractional foam drainage and KdV equations10.1155/2013/414353 ↗
48. Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique10.1186/s13662-015-0558-8 ↗
49. A novel method for a fractional derivative with non-local and non-singular kernel10.1016/j.chaos.2018.07.032 ↗
50. Approximate solutions for MHD squeezing fluid flow by a novel method10.1186/1687-2770-2014-18 ↗
51. On a fractional operator combining proportional and classical differintegrals10.3390/math8030360 ↗