[1] |
Kumar, M.; Yadav, N., Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey, Comput. Math. Appl., 62, 3796-3811 (2011) · Zbl 1236.65107 · doi:10.1016/j.camwa.2011.09.028 |
[2] |
Zou, Y.; Lie, G.; Shao, K.; Guo, Y.; Zhu, J.; Chen, X., Hybrid approach of radial basis function and finite element method for electromagnetic problems, IEEE Trans. Mag., 51, 1-4 (2015) |
[3] |
Han, H.; Chen, Q.; Qiao, J., Research on an online self-organizing radial basis function neural network, Neural Comput. Appl., 19, 667-676 (2010) · doi:10.1007/s00521-009-0323-6 |
[4] |
Duan, Y., A note on the meshless method using radial basis functions, Comput. Math. Appl., 55, 66-75 (2008) · Zbl 1176.65133 · doi:10.1016/j.camwa.2007.03.011 |
[5] |
Duan, Y.; Tan, Y-J, A meshless Galerkin method for Dirichlet problems using radial basis functions, J. Comput. Appl. Math., 196, 394-401 (2006) · Zbl 1106.65103 · doi:10.1016/j.cam.2005.09.018 |
[6] |
Chinchapatnam, PP; Djidjeli, K.; Nair, PB, Radial basis function meshless method for the steady incompressible Navier-Stokes equations, Int. J. Comput. Math., 84, 1509-1526 (2007) · Zbl 1123.76048 · doi:10.1080/00207160701308309 |
[7] |
Wendland, H., Meshless Galerkin methods using radial basis functions, Math. Comput., 68, 1521-2153 (1999) · Zbl 1020.65084 · doi:10.1090/S0025-5718-99-01102-3 |
[8] |
Zhang, X.; Song, KZ; Lu, MW; Liu, X., Mehsless methods based on collocation with radial basis functions, Comput. Mech., 26, 333-343 (2000) · Zbl 0986.74079 · doi:10.1007/s004660000181 |
[9] |
Oruc, O., Two meshless methods based on local radial basis function and barycentric rational interpolation for solving 2D viscoelastic wave equation, Comput. Math. Appl., 79, 3272-3288 (2020) · Zbl 1440.74466 · doi:10.1016/j.camwa.2020.01.025 |
[10] |
Waters, J.; Pepper, DW, Global versus localized RBF meshless methods for solving incompressible fluid flow with heat transfer, Numer. Heat Transf. B., 68, 185-203 (2015) · doi:10.1080/10407790.2015.1021590 |
[11] |
Schaback, R.; Wendland, H., Kernel techniques: from machine learning to meshless methods, Acta Numer., 15, 1-97 (2006) · Zbl 1111.65108 · doi:10.1017/S0962492906270016 |
[12] |
Kadalbajoo, MK; Kumar, A.; Tripathi, LP, Application of radial basis function with L-stable Padé time marching scheme for pricing exotic option, Comput. Math. Appl., 66, 500-511 (2013) · Zbl 1360.91154 · doi:10.1016/j.camwa.2013.06.002 |
[13] |
Sarra, SA, Integrated multiquadric radial basis function approximation methods, Comput. Math. Appl., 51, 500-511 (2006) · Zbl 1146.65327 · doi:10.1016/j.camwa.2006.04.014 |
[14] |
Fornberg, B.; Lehto, E.; Powell, C., Stable calculation of Gaussian-based RBF-FD stencils, Comput. Math. Appl., 65, 627-637 (2013) · Zbl 1319.65011 · doi:10.1016/j.camwa.2012.11.006 |
[15] |
Bouhamidi, A.; Hached, M.; Jbilou, K., A meshless RBF method for computing a numerical solution of unsteady Burgers’-type equations, Comput. Math. Appl., 68, 238-256 (2014) · Zbl 1369.65125 · doi:10.1016/j.camwa.2014.05.022 |
[16] |
Piret, C., The orthogonal gradients method: a radial basis functions method for solving partial differential equations on arbitrary surfaces, J. Comput. Phys., 231, 4662-4675 (2012) · Zbl 1248.35009 · doi:10.1016/j.jcp.2012.03.007 |
[17] |
Marchi, SD; Santin, G., A new stable basis for radial basis function interpolation, J. Comput. Appl. Math., 253, 1-13 (2013) · Zbl 1288.65013 · doi:10.1016/j.cam.2013.03.048 |
[18] |
Sarra, SA, A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains, Appl. Math. Comput., 218, 9853-9865 (2012) · Zbl 1245.65144 |
[19] |
Kazem, S.; Rad, JA, Radial basis functions method for solving of a non-local boundary value problem with Neumann’s boundary conditions, Appl. Math. Model., 36, 2360-2369 (2012) · Zbl 1246.65229 · doi:10.1016/j.apm.2011.08.032 |
[20] |
Kadem, A.; Baleanu, D., Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation, Commun. Nonlinear Sci. Numer. Simul., 15, 491-501 (2010) · Zbl 1221.45008 · doi:10.1016/j.cnsns.2009.05.024 |
[21] |
Baleanu, D.; Abadi, MH; Jajarmi, A.; Vahid, KZ; Nieto, JJ, A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects, Alexand. Eng. J., 61, 4779-4791 (2022) · doi:10.1016/j.aej.2021.10.030 |
[22] |
Baleanu, D.; Zibaei, S.; Namjoo, M.; Jajarmi, A., A nonstandard finite difference scheme for the modelling and nonidentical synchronization of a novel fractional chaotic system, Adv. Differ. Equ. (2021) · Zbl 1494.65060 · doi:10.1186/s13662-021-03454-1 |
[23] |
Erturk, VS; Godwe, E.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A., Novel fractional-order Lagrangian to describe motion of beam on nanowire, Acta Phys. Polonica A., 140, 265-272 (2021) · doi:10.12693/APhysPolA.140.265 |
[24] |
Jajarmi, A.; Baleanu, D.; Vahid, KZ; Pirouz, HM; Asad, JH, A new and general fractional Lagrangian approach: a capacitor microphone case study, Results Phys. (2021) · doi:10.1016/j.rinp.2021.104950 |
[25] |
Baleanu, D.; Etemad, S.; Rezapour, S., On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators, Alexand. Eng. J., 59, 3019-3027 (2020) · doi:10.1016/j.aej.2020.04.053 |
[26] |
Baleanu, D.; Etemad, S.; Pourrazi, S.; Rezapour, S., On the new fractional hybrid boundary value problems with three-point integral hybrid conditions, Adv. Differ. Equ. (2019) · Zbl 1487.34008 · doi:10.1186/s13662-019-2407-7 |
[27] |
Baleanu, D., Hedayati, V., Rezapour, S., Qurashi, M. M. A.: On two fraction differential inclusions. Springer, New York (2016). doi:10.1186/s40064-016-2564-z |
[28] |
Baleanu, D.; Etemad, S.; Rezapour, S., A hybrid Caputo fractional modelling for thermostat with hybrid boundary value conditions, Bound. Value Prob. (2020) · Zbl 1482.34016 · doi:10.1186/s13661-020-01361-0 |
[29] |
Mohammadi, H.; Kumar, S.; Rezapour, S.; Etemad, S., A theoretical study of the Caputo-Fabrizio fractional modelling for hearing loss due to Mumps virus with optimal control, Chaos Solitons Fractals. (2021) · doi:10.1016/j.chaos.2021.110668 |
[30] |
Alizadeh, S.; Baleanu, D.; Rezapour, S., Analyzing transient response of the parallel RCL circuit by using the Caputo-Fabrizio fractional derivative, Adv. Differ. Equ. (2020) · Zbl 1487.94202 · doi:10.1186/s13662-020-2527-0 |
[31] |
Matar, MM; Abbas, MI; Alzabut, J.; Kabar, MKA; Etemad, S.; Rezapour, S., Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives, Adv. Differ. Equ. (2021) · Zbl 1487.34028 · doi:10.1186/s13662-021-03228-9 |
[32] |
Baleanu, D.; Rezapour, S.; Saberpour, Z., On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation, Bound. Value Probl. (2019) · Zbl 1524.45012 · doi:10.1186/s13661-019-1194-0 |
[33] |
Aydogan, MS; Baleanu, D.; Mousalou, A.; Rezapour, S., On higher order integro-differential equations including the Caputo-Fabrizio derivative, Bound. Value Probl. (2018) · Zbl 1422.34019 · doi:10.1186/s13661-018-1008-9 |
[34] |
Baleanu, D.; Mohammadi, H.; Rezapour, S., Analysis of the model of HIV-1 infection of CD4+ T-Cell with a new approach of fractional derivative, Adv. Differ. Equ. (2020) · Zbl 1482.37090 · doi:10.1186/s13662-020-02544-w |
[35] |
Hodges, HD; Rutkowski, MJ, Free-vibration analysis of rotating beams by a variable-order finite element method, AIAA J., 19, 1459-1466 (1981) · Zbl 0468.73093 · doi:10.2514/3.60082 |
[36] |
Nagaraj, VT; Shanthakumar, P., Rotor blade vibration by the Galerkin finite element method, J. Sound Vib., 43, 575-577 (1975) · doi:10.1016/0022-460X(75)90013-9 |
[37] |
Bauchau, OA; Hong, CH, Finite element approach to rotor blade modeling, J. Am. Helicop. Soc., 32, 60-67 (1987) · doi:10.4050/JAHS.32.60 |
[38] |
Hoa, SV, Vibration of a rotating beam with tip mass, J. Sound Vib., 67, 369-381 (1979) · Zbl 0428.73059 · doi:10.1016/0022-460X(79)90542-X |
[39] |
Raju, I. S., Phillips, D. R., Krishnamurthy, T.: A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems. Comput. Mech. 34, 464-474 (2204) · Zbl 1109.74375 |
[40] |
Wang, G.; Wereley, NM, Free vibration analysis of rotating blades with uniform tapers, AIAA J., 42, 2429-2437 (2004) · doi:10.2514/1.4302 |