Novel soliton solutions of the generalized (3+1)-dimensional conformable KP and KP–BBM equations

[1] Şenol, B., & Demiroğlu, U. (2019). Frequency frame approach on loop shaping of first order plus time delay systems using fractional order PI controller. ISA transactions, 86, 192-200.

[2] He, J.H., & Ji, F.Y. (2019). Two-scale mathematics and fractional calculus for thermodynamics. Thermal Science, 23(4), 2131-2133.

[3] Wang, G., Liu, Y., Wu, Y., & Su, X. (2020). Symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics. Fractals, 28(3), 2050044-134.

[4] Kumar, A., Komaragiri, R., & Kumar, M. (2019). Design of efficient fractional operator for ECG signal detection in implantable cardiac pacemaker systems. International Journal of Circuit Theory and Applications, 47(9), 1459-1476.

[5] Mashayekhi, S., Hussaini, M.Y., & Oates, W. (2019). A physical interpretation of fractional viscoelasticity based on the fractal structure of media: theory and experimental validation. Journal of the Mechanics and Physics of Solids, 128, 137-150.

[6] Abdou, M.A. (2019). On the fractional order space-time nonlinear equations arising in plasma physics. Indian Journal of Physics, 93(4), 537-541.

[7] Iyiola, O.S., Oduro, B., & Akinyemi, L. (2021). Analysis and solutions of generalized Chagas vectors reinfestation model of fractional order type. Chaos, Solitons Fractals, 145, 110797.

[8] Owusu-Mensah, I., Akinyemi, L., Oduro, B., & Iyiola, O.S. (2020). A fractional order approach to modeling and simulations of the novel COVID-19. Adv. Differ. Equ., 2020(1), 1-21. https://doi.org/10.1186/s13662-020-03141-7. Epub 2020 Dec 3. PMID: 33288983; PMCID: PMC7711272

[9] Pellegrino, E., Pezza, L., & Pitolli, F. (2020). A collocation method in spline spaces for the solution of linear fractional dynamical systems. Mathematics and Computers in Simulation, 176, 266-278.

[10] Tasbozan, O., Çenesiz, Y., Kurt, A., & Baleanu, D. (2017). New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method. Open Physics, 15(1), 647-651.

[11] Rezazadeh, H. (2018). New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik, 167, 218-227.

[12] Vahidi, J., Zabihi, A., Rezazadeh, H., & Ansari, R. (2021). New extended direct algebraic method for the resonant nonlinear Schrödinger equation with Kerr law nonlinearity. Optik, 227, 165936.

[13] Senol, M. (2020). New analytical solutions of fractional symmetric regularized-long-wave equation. Revista Mexicana de Fisica, 66(3 May-Jun), 297-307.

[14] Rezazadeh, H., Ullah, N., Akinyemi, L., Shah, A., Mirhosseini-Alizamin, S.M., Chu, Y.M., & Ahmad, H. (2021). Optical soliton solutions of the generalized non-autonomous nonlinear Schrödinger equations by the new Kudryashov's method. Results in Phys., 24, 104179.

[15] Osman, M.S., Korkmaz, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., & Zhou, Q. (2018). The unified method for conformable time fractional Schrödinger equation with perturbation terms. Chinese Journal of Physics, 56(5), 2500-2506.

[16] Kolebaje, O., Bonyah, E., & Mustapha, L. (2019). The first integral method for two fractional non-linear biological models. Discrete Continuous Dynamical Systems-S, 12(3), 487.

[17] Ghanbari, B., Osman, M. S., & Baleanu, D. (2019). Generalized exponential rational function method for extended Zakharov-Kuzetsov equation with conformable derivative. Modern Physics Letters A, 34(20), 1950155.

[18] Akinyemi, L., Senol, M., & Iyiola, O.S. (2021). Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method, Math. Comput. Simul., 182, 211-233. https://doi.org/10.1016/j.matcom.2020.10.017

[19] Senol, M., Akinyemi, L., Ata, A., & Iyiola, O.S. (2021). Approximate and generalized solutions of conformable type Coudrey-Dodd-Gibbon-Sawada-Kotera equation. International Journal of Modern Physics B, 35(02), 2150021.

[20] Rezazadeh, H., Inc, M., & Baleanu, D. (2020). New Solitary Wave Solutions for Variants of (3+1)- Dimensional Wazwaz-Benjamin-Bona-Mahony Equations. Frontiers in Phys., 8, 1-11.

[21] Seadawy, A.R., Ali, K.K., & Nuruddeen, R.I. (2019). A variety of soliton solutions for the fractional Wazwaz-Benjamin-Bona-Mahony equations. Results Phys., 12, 2234-2241.

[22] Az-Zo’bi, E.A. (2019). New kink solutions for the van der Waals p‐system, Mathematical Methods in the Applied Sciences, 42(18), 6216-6226.

[23] Az-Zo’bi, E.A. (2019). Peakon and solitary wave solutions for the modified Fornberg-Whitham equation using simplest equation method. International Journal of Mathematics and Computer Sci., 14(3), 635-645.

[24] Az-Zo’bi, E.A., AlZoubi, W.A., Akinyemi, L., et al. (2021). Abundant closed-form solitons for timefractional integro–differential equation in fluid dynamics. Opt. Quant. Electron, 53, 132. https://doi.org/10.1007/s11082-021-02782-6

[25] Vahidi, J., Zekavatmand, S.M., Rezazadeh, H., Inc, M., Akinlar, M.A., & Chu, Y.M. (2021). New solitary wave solutions to the coupled Maccari’s system. Results in Physics, 21, 103801.

[26] Akinyemi, L., Senol, M., Mirzazadeh, M., & Eslami, M. (2021). Optical solitons for weakly nonlocal Schrödinger equation with parabolic law nonlinearity and external potential. Optik, 230 1-9.

[27] Leta, T.D., Liu, W., El Achab, A., & Rezazadeh, H. (2021). A Bekir Dynamical Behavior of Traveling Wave Solutions for a (2+1)-Dimensional Bogoyavlenskii Coupled System. Qualitative Theory of Dynamical Systems, 20(1), 1-22.

[28] Biswas, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S.P., & Belic, M. (2018). Optical solitons having weak non-local nonlinearity by two integration schemes, Optik, 164 380–384.

[29] Hosseini, K., Salahshour, S., & Mirzazadeh, M. (2021). Bright and dark solitons of a weakly nonlocal Schrödinger equation involving the parabolic law nonlinearity. Optik, 227, 166042.

[30] Hosseini, K., Mirzazadeh, M., & Gómez-Aguilar, J.F. (2020). Soliton solutions of the Sasa–Satsuma equation in the monomode optical fibers including the beta-derivatives. Optik, 224, 165425.

[31] Hosseini, K., Mirzazadeh, M., Vahidi, J., & Asghari, R. (2020). Optical wave structures to the Fokas– Lenells equation. Optik, 207, 164450.

[32] Hosseini, K., Mirzazadeh, M., Ilie, M., & Gómez-Aguilar, J.F. (2020). Biswas–Arshed equation with the beta time derivative: optical solitons and other solutions. Optik, 217, 164801.

[33] Hosseini, K., Mirzazadeh, M., Rabiei, F., Baskonus, H.M., & Yel, G. (2020). Dark optical solitons to the Biswas–Arshed equation with high order dispersions and absence of the self-phase modulation. Optik, 209, 164576.

[34] Akinyemi, L., Şenol, M., Rezazadeh, H., Ahmad, H., & Wang, H. (2021). Abundant optical soliton solutions for an integrable (2+1)-dimensional nonlinear conformable Schrödinger system. Results in Phys. 104177. https://doi.org/10.1016/j.rinp.2021.104177

[35] El-Tawil M.A. & Huseen S.N. (2012). The Q-homotopy analysis method (q-HAM). Int. J. Appl. Math. Mech., 8 (15), 51-75.

[36] Akinyemi L. (2019). q-Homotopy analysis method for solving the seventh-order time-fractional Lax's Korteweg–de Vries and Sawada–Kotera equations. Comp. Appl. Math., 38(4), 1-22.

[37] Akinyemi L., Iyiola O.S., & Akpan U. (2020). Iterative methods for solving fourth- and sixth order timefractional Cahn-Hillard equation. Math. Meth. Appl. Sci., 43(7), 4050–4074. https://doi.org/10.1002/mma.6173

[38] Az-Zo’bi, E.A. (2018). A reliable analytic study for higher-dimensional telegraph equation, Journal of Mathematics and Computer Science, 18, 423–429.

[39] Senol M., Iyiola O.S., Daei Kasmaei H., & Akinyemi L. (2019). Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent-Miodek system with energy-dependent Schrödinger potential. Adv. Differ. Equ., 2019, 1-21.

[40] Senol, M., Tasbozan, O., & Kurt, A. (2019). Numerical solutions of fractional Burgers' type equations with conformable derivative. Chinese Journal of Physics, 58, 75-84.

[41] Senol, M., Kurt, A., Atilgan, E., & Tasbozan, O. (2019). Numerical solutions of fractional BoussinesqWhitham-Broer-Kaup and diffusive Predator-Prey equations with conformable derivative. New Trends in Mathematical Sciences, 7(3), 286-300.

[42] Senol M. (2020). Analytical and approximate solutions of (2+1)-dimensional time-fractional BurgersKadomtsev-Petviashvili equation. Commun. Theor. Phys., 72(5), 1-11.

[43] Johnston, S.J., Jafari, H., Moshokoa, S.P., Ariyan, V.M., & Baleanu, D. (2016). Laplace homotopy perturbation method for Burgers equation with space-and time-fractional order. Open Physics, 14(1), 247-252.

[44] Akinyemi L. & Iyiola O.S. (2020). Exact and approximate solutions of time-fractional models arising from physics via Shehu transform. Math. Meth. Appl. Sci., 43(12), 7442-7464. https://doi.org/10.1002/mma.6484

[45] Akinyemi L. (2020). A fractional analysis of Noyes–Field model for the nonlinear Belousov–Zhabotinsky reaction. Comp. Appl. Math., 39, 1-34. https://doi.org/10.1007/s40314-020-01212-9

[46] Akinyemi L. & Huseen S.N., (2020). A powerful approach to study the new modified coupled Korteweg–de Vries system. Math. Comput. Simul., 177, 556-567. https://doi.org/10.1016/j.matcom.2020.05.021

[47] Akinyemi L. & Iyiola O.S. (2020). A reliable technique to study nonlinear time-fractional coupled Korteweg-de Vries equations. Adv. Differ. Equ., 2020, 1-27. https://doi.org/10.1186/s13662-020-02625-w

[48] Adomian G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer.

[49] Az-Zo’bi, E.A. (2014). An Approximate Analytic Solution for Isentropic Flow by An Inviscid Gas Equations, Archives of Mechanics, 66(3), 203-212.

[50] Az-Zo’bi, E.A. (2013). Construction of Solutions for Mixed Hyperbolic Elliptic Riemann Initial Value System of Conservation Laws, Applied Mathematical Modeling, 37, 6018-6024.

[51] Az-Zo’bi, E.A., Al Dawoud K., & Marashdeh, M.F. (2015). Numeric-analytic solutions of mixed-type systems of balance laws, Applied Mathematics and Comput., 265, 133–143.

[52] Akinyemi, L., Senol, M., & Huseen, S.N. (2021). Modified homotopy methods for generalized fractional perturbed Zakharov-Kuznetsov equation in dusty plasma. Adv. Differ. Equ. 2021(1), 1-27.
https://doi.org/10.1186/s13662-020-03208-5

[53] Wazwaz A.M. & El-Tantawy S. (2016). A new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation. Nonlinear Dyn., 84, 1107–1112.

[54] Khalil R., Al Horani M., Yousef A., & Sababheh M. (2014). A new definition of fractional derivative. J. Comput. Appl. Math., 264, 65-70.

[55] Abdeljawad T. (2015). On conformable fractional calculus. J. Comput. Appl. Math., 279, 57–66.

[56] El-Ganaini S. & Al-Amr M.O. (2019). New abundant wave solutions of the conformable space-time fractional (4+1)-dimensional Fokas equation in water waves. Comput. Math. Appl., 78(6), 2094-2106. https://doi.org/10.1016/j.camwa.2019.03.050

[57] Bekir A. & Guner O. (2013). Bright and dark soliton solutions of the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation and generalized Benjamin equation. Pramana- J. Phys., 81, 203-214.

[58] Taghizadeh N., Mirzazadeh M., & Noori S.R.M. (2012). Exact solutions of the generalized Benjamin equation and (3+1)-dimensional Gkp equation by the extended tanh method. Appl. Math. Int. J., 7(1), 175-187.

[59] Wazwaz A.M. (2005). Exact solutions of compact and noncompact structures for the KP-BBM equation. Appl. Math. Comput., 169(1), 700-712.

[60] Wazwaz A.M. (2012). Multiple-soliton solutions for a (3+1)-dimensional generalized KP equation. Commun. Nonlinear Sci. Numer. Simul., 17, 491–495.

[61] Wazwaz A.M. (2011). Multi-front waves for extended form of modified Kadomtsev-Petviashvili equations. Appl. Math. Mech., 32(7), 875–880.