[1] E. Bas, R. Ozarslan, Real world applications of fractional models by Atangana–Baleanu fractional
derivative, Chaos Solit. Fractals 116 (2018) 121–125.
[2] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog.
Fract. Differ. Appl. 1 (2015) 73–85.
[3] M. Dehghan, M. Abbaszadeh, The use of proper orthogonal decomposition (POD) meshless RBF-
FD technique to simulate the shallow water equations, J. Comput. Phys. 351 (2017) 478–510.
[4] R.T. Farouki, The Bernstein polynomial basis: A centennial retrospective, Comput. Aided Geom.
Des. 29, (2012) 379–419.
[5] A.K. Gupta, S.S. Ray, On the solution of time-fractional KdV–Burgers equation using
Petrov–Galerkin method for propagation of long wave in shallow water, Chaos Solit. Fractals
116 (2018) 376–380.
[6] A.H. Hadian-Rasanan, N. Bajalan, K. Parand, J.A. Rad, Simulation of nonlinear fractional dynam-
ics arising in the modeling of cognitive decision making using a new fractional neural network,
Math. Methods Appl. Sci. 43 (2020) 1437–1466.
[7] A.H. Hadian-Rasanan, D. Rahmati, S. Gorgin, K. Parand, A single layer fractional orthogonal
neural network for solving various types of LaneEmden equation, New Astron. 1 (2020) 101307.
[8] M. Jani, E. Babolian, S. Javadi, Bernstein modal basis: Application to the spectral Petrov-Galerkin
method for fractional partial differential equations, Math. Methods Appl. Sci. 40 (2017) 7663–
7672.
[9] M. Jani, E. Babolian, S. Javadi, D. Bhatta, Banded operational matrices for Bernstein polynomials
and application to the fractional advection-dispersion equation, Numer. Algorithms 75 (2017)
1041–1063.
[10] B. Jin, R. Lazarov, Z. Zhou, Two fully discrete schemes for fractional diffusion and diffusion-wave
equations with nonsmooth data, SIAM J. Sci. Comput. 38 (2016) A146–A170.
[11] B. Juttler, The dual basis functions for the Bernstein polynomials, Adv. Comput. Math. 8 (1998)
345–352.
[12] D. Kaya, S. Glbahar, A. Yokus¸, M. Glbahar, Solutions of the fractional combined KdV–mKdV
equation with collocation method using radial basis function and their geometrical obstructions,
Adv. Differ. Equ. 1 (2018) 77.
[13] NR. Kevlahan, R. Khan, B. Protas, On the convergence of data assimilation for the one-
dimensional shallow water equations with sparse observations, Adv. Comput. Math. 45 (2019)
3195–3216.
[14] M.M. Khader, K.M. Saad, Z. Hammouch, D. Baleanu, A spectral collocation method for solving
fractional KdV and KdV-Burgers equations with non-singular kernel derivatives, Appl. Numer.
Math. 161 (2021) 137–146.
[15] A. Kurganov, Finite-volume schemes for shallow-water equations, Acta Numer. 27 (2018) 289–
351.
[16] J. Li, J. Chen, B. Li, Gradient-optimized physics-informed neural networks (GOPINNs): a deep
learning method for solving the complex modified KdV equation, Nonlinear Dyn. 107 (2022) 781–
792.
[17] Y. Lin, C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation,
J. Comput. Phys. 225 (2007) 1533–1552.
[18] G.G. Lorentz, Approximation of Functions, American Mathematical Scociety, 2023.
[19] F. Mainardi, Why the Mittag-Leffler function can be considered the Queen function of the Frac-
tional Calculus? Entropy, 22 (2020) 1359.
[20] S. Mehrkanoon, T. Falck, J.A. Suykens, Approximate solutions to ordinary differential equations
using least squares support vector machines, IEEE Trans. Neural Netw. Learn. Syst. 23 (2012)
1356–1367.
[21] S. Mehrkanoon, S. Mehrkanoon, J.A. Suykens, Parameter estimation of delay differential equa-
tions: an integration-free LS-SVM approach, Commun. Nonlinear Sci. Numer. Simul. 19 (2014)
830–841.
[22] S. Mehrkanoon, J.A. Suykens, Learning solutions to partial differential equations using LS-SVM,
Neurocomputing 159 (2015) 105–116.
[23] V.H. Moghaddam, J. Hamidzadeh, New Hermite orthogonal polynomial kernel and combined
kernels in support vector machine classifier, Pattern Recognit. 60 (2016) 921–935.
[24] A. Pakniyat, K. Parand, M. Jani, Least squares support vector regression for differential equations
on unbounded domains, Chaos Solit. Fractals. 151 (2021) 111232.
[25] K. Parand, A.A. Aghaei, M. Jani, A. Ghodsi, A new approach to the numerical solution of Fredholm
integral equations using least squares-support vector regression, Math. Comput. Simul. 180 (2021)
114–128.
[26] K. Parand, A.A. Aghaei, M. Jani, A. Ghodsi, Parallel LS-SVM for the numerical simulation of
fractional Volterra’s population model, Alex. Eng. J. 60 (2021) 5637–5647.
[27] K. Parand, M. Razzaghi, R. Sahleh, M. Jani, Least squares support vector regression for solving
Volterra integral equations, Eng. Comput. 9 (2020) 789–796.
[28] J.A. Rad, K. Parand, S. Chakraverty, Learning with Fractional Orthogonal Kernel Classifiers in
Support Vector Machines: Theory, algorithms and applications, Springer, 2023.
[29] Z. Yu, J. Sun, B. Wu, A space–time spectral Petrov–Galerkin method for nonlinear time-fractional
Korteweg–de Vries–Burgers equations, Math. Methods Appl. Sci. 44 (2021) 4348–4365.
[30] H. Zhang, SJ. Cai, JY. Li, Y. Liu, ZY. Zhang, Enforcing generalized conditional symmetry in
physics-informed neural network for solving the KdV-like equation with Robin initial/boundary
conditions, Nonlinear Dyn.111 (2023) 10381–10392.
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