Page 53 - IJOCTA-15-1
P. 53
Approximate analytical solutions of fractional coupled Whitham-Broer-Kaup equations . . .
Analysis in Medicine and Biology, 2(3). https: https://doi.org/10.11121/ijocta.2023.1
//doi.org/10.15761/FGNAMB.1000140 366
[10] Gour, M. M., Yadav, L. K., Purohit, S. D., & [20] Sene, N. (2022). Theory and applications of new
Suthar, D. L. (2023). Homotopy decomposition fractional-order chaotic system under Caputo op-
method to analysis fractional hepatitis B virus erator. An International Journal of Optimization
infection model. Applied Mathematics in Science and Control: Theories & Applications (IJOCTA),
and Engineering, 31(1). https://doi.org/10.1 12(1), 20-38. https://doi.org/10.11121/ijo
080/27690911.2023.2260075 cta.2022.1108
[11] Veeresha, P., & Prakasha, D. G. (2020). An ef- [21] Kazem, S. (2013). Exact solution of some linear
ficient technique for two-dimensional fractional fractional differential equations by Laplace trans-
order biological population model. International form. International Journal of Nonlinear Sci-
Journal of Modeling, Simulation, and Scientific ences, 16(1), 3-11.
Computing, 11, 2050005. https://doi.org/10 [22] Kumar, S. (2014). A new analytical modelling for
.1142/S1793962320500051 fractional telegraph equation via Laplace trans-
[12] Sheergojri A., Iqbal P., Agarwal P., & Ozdemir form. Applied Mathematical Modelling, 38, 3154-
N. (2022). Uncertainty-based Gompertz growth 3163. https://doi.org/10.1016/j.apm.2013
model for tumor population and its numeri- .11.035
cal analysis. An International Journal of Opti- [23] Agarwal, G., Yadav, L.K., Albalawi, W., Abdel-
mization and Control: Theories & Applications Aty, A.H., Nisar K.S., & Shefeeq, T. (2022).
(IJOCTA), 12, 137-150. https://doi.org/10.1 Two analytical approaches for space-and time-
1121/ijocta.2022.1208 fractional coupled burger’s equations via Elzaki
[13] Nasrolahpour, H. (2013). A note on fractional transform. Progress in Fractional Differentiation
electrodynamics. Communications in Nonlinear and Applications, 8(1), 177-190. https://doi.or
Science and Numerical Simulation, 18, 2589-2593. g/10.18576/pfda/080111
https://doi.org/10.1016/j.cnsns.2013.01. [24] Neamaty, A., Agheli, B., & Darzi, R. (2016). Ap-
005 plications of homotopy perturbation method and
[14] Drapaca, C. S., & Sivaloganathan, S. (2012). A Elzaki transform for solving nonlinear partial dif-
fractional model of continuum mechanics. Jour- ferential equations of fractional order. Journal of
nal of Elasticity, 107, 105-123. https://doi.or Nonlinear Evolution Equations and Applications,
g/10.1007/s10659-011-9346-1 6, 91-104.
[15] Kumar, D., Seadwy, A. R., & Joarder, A. K. [25] Yang, X. J. (2016). A new integral transform
(2018). Modified kudryashov method via new ex- method for solving steady heat-transfer problem.
act solutions for some conformable fractional dif- Thermal Science, 20, 639-642. https://doi.or
ferential equations arising in mathematical biol- g/10.2298/TSCI16S3639Y
ogy. Chinese Journal of Physics, 56(1), 75-85. ht [26] Aboodh, K.S. (2013). The new integral transform
tps://doi.org/10.1016/j.cjph.2017.11.020 ”Aboodh Transform”. Global Journal of Pure and
[16] Baleanu, D., Wu, G. C., & Zeng, S. D. (2017). Applied Mathematics, 9(1), 35-43.
Chaos analysis and asymptotic stability of gen- [27] Kili¸cman, A., & Gadain, H. E. (2010). On the
eralized Caputo fractional differential equations. applications of Laplace and Sumudu transforms.
Chaos, Solitons & Fractals, 102, 99-105. https: Journal of the Franklin Institute, 347, 848-862.
//doi.org/10.1016/j.chaos.2017.02.007 https://doi.org/10.1016/j.jfranklin.2010
[17] Demirtas, M., & Ahmad, F. (2023). Fractional .03.008
fuzzy PI controller using particle swarm opti- [28] Guo, S. M., Mei, L. Q., Li, Y., & Sun, Y.
mization to improve power factor by boost con- F. (2012). The improved fractional sub-equation
verter, An International Journal of Optimization method and its applications to the space-time
and Control:Theories & Applications (IJOCTA), fractional differential equations in fluid mechan-
13(2), 205-213. https://doi.org/10.11121/i ics. Physics Letters A, 376, 407-411. https://do
jocta.2023.1260 i.org/10.1016/j.physleta.2011.10.056
[18] Tajadodi, H., Jafari, H., & Ncube, M. N. (2022). [29] Whitham, G. B. (1967). Variational methods and
Genocchi polynomials as a tool for solving a class applications to water waves. Proceedings of the
of fractional optimal control problems, An In- Royal Society of London. Series A. Mathemat-
ternational Journal of Optimization and Control: ical and Physical Sciences, 299, 6-25. https:
Theories & Applications (IJOCTA), 12(2), 160- //doi.org/10.1098/rspa.1967.0119
168. https://doi.org/10.11121/ijocta.2022 [30] Broer, L. J. F. (1975). Approximate equations for
.1263 long water waves. Applied Scientific Research, 31,
[19] Uzun, P. Y., Uzun, K., & Koca, I. (2023). 377-395. https://doi.org/10.1007/BF004180
The effect of fractional order mathematical mod- 48
elling for examination of academic achievement [31] Kaup, D. J. (1975). A higher-order water-wave
in schools with stochastic behaviors, An Interna- equation and the method for solving it. Progress
tional Journal of Optimization and Control: The- of Theoretical Physics, 54, 396-408. https://do
ories & Applications (IJOCTA),13(2), 244-258. i.org/10.1143/PTP.54.396
47

