[1] |
Alkasassbeh, M.; Omar, Z.; Mebarek-Oudina, F.; Raza, J.; Chamkha, A., Heat transfer study of convective fin with temperature-dependent internal heat generation by hybrid block method, Heat Transf. Asian Res., 48, 4, 1225-1244 (2019) · doi:10.1002/htj.21428 |
[2] |
Atanackovic, T.; Budincevic, M.; Pilipovic, S., On a fractional distributed-order oscillator, J. Phys. A Math. Gen., 38, 30, 6703 (2005) · Zbl 1074.74030 · doi:10.1088/0305-4470/38/30/006 |
[3] |
Atanackovic, TM, On a distributed derivative model of a viscoelastic body, C.R. Mec., 331, 10, 687-692 (2003) · Zbl 1177.74093 · doi:10.1016/j.crme.2003.08.003 |
[4] |
Atanacković, TM; Oparnica, L.; Pilipović, S., On a nonlinear distributed order fractional differential equation, J. Math. Anal. Appl., 328, 1, 590-608 (2007) · Zbl 1115.34005 · doi:10.1016/j.jmaa.2006.05.038 |
[5] |
Clarke, FH; Ledyaev, YS; Stern, RJ; Wolenski, PR, Nonsmooth Analysis and Control Theory (2008), Berlin: Springer Science & Business Media, Berlin · Zbl 1047.49500 |
[6] |
Dadkhah, E.; Shiri, B.; Ghaffarzadeh, H.; Baleanu, D., Visco-elastic dampers in structural buildings and numerical solution with spline collocation methods, J. Appl. Math. Comput., 63, 1, 29-57 (2020) · Zbl 1490.74071 · doi:10.1007/s12190-019-01307-5 |
[7] |
Diethelm, K.; Ford, NJ, Numerical analysis for distributed-order differential equations, J. Comput. Appl. Math., 225, 1, 96-104 (2009) · Zbl 1159.65103 · doi:10.1016/j.cam.2008.07.018 |
[8] |
Efe, MÖ, Integral sliding mode control of a quadrotor with fractional order reaching dynamics, Trans. Inst. Meas. Control., 33, 8, 985-1003 (2011) · doi:10.1177/0142331210377227 |
[9] |
Farhan, M.; Omar, Z.; Mebarek-Oudina, F.; Raza, J.; Shah, Z.; Choudhari, R.; Makinde, O., Implementation of the one-step one-hybrid block method on the nonlinear equation of a circular sector oscillator, Comput. Math. Model., 31, 1, 116-132 (2020) · Zbl 1441.65063 · doi:10.1007/s10598-020-09480-0 |
[10] |
Fernández-Anaya, G.; Nava-Antonio, G.; Jamous-Galante, J.; Muñoz-Vega, R.; Hernández-Martínez, E., Asymptotic stability of distributed order nonlinear dynamical systems, Commun. Nonlinear Sci. Numer. Simul., 48, 541-549 (2017) · Zbl 1510.34112 · doi:10.1016/j.cnsns.2017.01.020 |
[11] |
Jakovljević, B.; Pisano, A.; Rapaić, MR; Usai, E., On the sliding-mode control of fractional-order nonlinear uncertain dynamics, Int. J. Robust Nonlinear Control, 26, 4, 782-798 (2016) · Zbl 1333.93071 · doi:10.1002/rnc.3337 |
[12] |
Jensen, J.L.W.V.: Om konvekse funktioner og uligheder imellem middelvaerdier. Nyt Tidsskrift for Matematik 30, 49-69 (1905) https://www.jstor.org/stable/24528332 |
[13] |
Jensen, JLWV, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math., 30, 175-193 (1906) · JFM 37.0422.02 · doi:10.1007/BF02418571 |
[14] |
Jiao, Z.; Chen, YQ, Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders, Comput. Math. Appl., 64, 10, 3053-3058 (2012) · Zbl 1268.34018 · doi:10.1016/j.camwa.2011.10.014 |
[15] |
Jiao, Z., Chen, Y.Q., Podlubny, I.: Distributed-order dynamic systems: stability. Simulation, Applications and Perspectives, London (2012) · Zbl 1401.93005 |
[16] |
Kamal, S., Chalanga, A., Moreno, J.A., Fridman, L., Bandyopadhyay, B.: Higher order super-twisting algorithm. In: 2014 13th International Workshop on Variable Structure Systems (VSS), IEEE, pp 1-5 (2014) |
[17] |
Kochubei, AN, Distributed order calculus and equations of ultraslow diffusion, J. Math. Anal. Appl., 340, 1, 252-281 (2008) · Zbl 1149.26014 · doi:10.1016/j.jmaa.2007.08.024 |
[18] |
Lazović, G.; Vosika, Z.; Lazarević, M.; Simić-Krstić, J.; Koruga, D., Modeling of bioimpedance for human skin based on fractional distributed-order modified cole model, FME Transact., 42, 1, 74-81 (2014) · doi:10.5937/fmet1401075L |
[19] |
Li, A.; Liu, G.; Luo, Y.; Yang, X., An indirect lyapunov approach to robust stabilization for a class of linear fractional-order system with positive real uncertainty, J. Appl. Math. Comput., 57, 1, 39-55 (2018) · Zbl 1393.93100 · doi:10.1007/s12190-017-1093-4 |
[20] |
Li, Y.; Chen, Y., Theory and implementation of distributed-order element networks, Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf., 54808, 361-367 (2011) |
[21] |
Li, Y., Chen, Y.Q.: Theory and implementation of weighted distributed order integrator. In: IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications, IEEE, pp 119-124 (2012) |
[22] |
Liu, L.; Feng, L.; Xu, Q.; Zheng, L.; Liu, F., Flow and heat transfer of generalized maxwell fluid over a moving plate with distributed order time fractional constitutive models, Int. Commun. Heat Mass Transf., 116, 104679 (2020) · doi:10.1016/j.icheatmasstransfer.2020.104679 |
[23] |
Mahmoud, GM; Farghaly, AA; Abed-Elhameed, TM; Aly, SA; Arafa, AA, Dynamics of distributed-order hyperchaotic complex van der pol oscillators and their synchronization and control, Eur. Phys. J. Plus, 135, 1, 1-16 (2020) · doi:10.1140/epjp/s13360-019-00006-1 |
[24] |
Mebarek-Oudina, F., Numerical modeling of the hydrodynamic stability in vertical annulus with heat source of different lengths, Eng. Sci. Technol. Int. J., 20, 4, 1324-1333 (2017) |
[25] |
Morgado, ML; Rebelo, M., Numerical approximation of distributed order reaction-diffusion equations, J. Comput. Appl. Math., 275, 216-227 (2015) · Zbl 1298.35242 · doi:10.1016/j.cam.2014.07.029 |
[26] |
Muñoz-Vázquez, AJ; Parra-Vega, V.; Sánchez-Orta, A., A novel continuous fractional sliding mode control, Int. J. Syst. Sci., 48, 13, 2901-2908 (2017) · Zbl 1386.93067 · doi:10.1080/00207721.2017.1348564 |
[27] |
Muñoz-Vázquez, AJ; Parra-Vega, V.; Sánchez-Orta, A., Non-smooth convex Lyapunov functions for stability analysis of fractional-order systems, Trans. Inst. Meas. Control., 41, 6, 1627-1639 (2019) · doi:10.1177/0142331218785694 |
[28] |
Muñoz-Vázquez, AJ; Fernández-Anaya, G.; Sánchez-Torres, JD; Meléndez-Vázquez, F., Predefined-time control of distributed-order systems, Nonlinear Dyn., 103, 3, 2689-2700 (2021) · Zbl 1517.93014 · doi:10.1007/s11071-021-06264-y |
[29] |
Nesterov, Y., Introductory Lectures on Convex Optimization: A Basic Course (2013), Berlin: Springer Science & Business Media, Berlin · Zbl 1086.90045 |
[30] |
Patnaik, S.; Semperlotti, F., Application of variable-and distributed-order fractional operators to the dynamic analysis of nonlinear oscillators, Nonlinear Dyn., 100, 1, 561-580 (2020) · doi:10.1007/s11071-020-05488-8 |
[31] |
Pérez-Ventura, U.; Fridman, L., Design of super-twisting control gains: a describing function based methodology, Automatica, 99, 175-180 (2019) · Zbl 1406.93076 · doi:10.1016/j.automatica.2018.10.023 |
[32] |
Pisano, A.; Rapaić, MR; Jeličić, ZD; Usai, E., Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics, Int. J. Robust Nonlinear Control, 20, 18, 2045-2056 (2010) · Zbl 1207.93079 · doi:10.1002/rnc.1565 |
[33] |
Pisano, A., Rapaić, M.R., Usai, E., Jeličić, Z.D.: Continuous finite-time stabilization for some classes of fractional order dynamics. In: International Workshop on Variable Structure Systems, IEEE, pp 16-21 (2012) |
[34] |
Podlubny, I., Fractional Differential Equations (1998), Amsterdam: Elsevier, Amsterdam · Zbl 0922.45001 |
[35] |
Rayal, A.; Verma, SR, An approximate wavelets solution to the class of variational problems with fractional order, J. Appl. Math. Comput., 65, 1, 735-769 (2021) · Zbl 1475.34008 · doi:10.1007/s12190-020-01413-9 |
[36] |
Ross, B.; Samko, SG; Love, ER, Functions that have no first order derivative might have fractional derivatives of all orders less than one, Real Anal. Exch., 20, 1, 140-157 (1994) · Zbl 0820.26002 · doi:10.2307/44152475 |
[37] |
Taghavian, H.; Tavazoei, MS, Stability analysis of distributed-order nonlinear dynamic systems, Int. J. Syst. Sci., 49, 3, 523-536 (2018) · Zbl 1385.93066 · doi:10.1080/00207721.2017.1412535 |
[38] |
Toaldo, B., Lévy mixing related to distributed order calculus, subordinators and slow diffusions, J. Math. Anal. Appl., 430, 2, 1009-1036 (2015) · Zbl 1319.60100 · doi:10.1016/j.jmaa.2015.05.024 |
[39] |
Wang, F., Liu, X.: Pseudo-state estimation for fractional order neural networks. Neural Process. Lett. pp 1-14 (2021) |
[40] |
Wei, L.; Liu, L.; Sun, H., Stability and convergence of a local discontinuous galerkin method for the fractional diffusion equation with distributed order, J. Appl. Math. Comput., 59, 1, 323-341 (2019) · Zbl 1422.65271 · doi:10.1007/s12190-018-1182-z |
[41] |
Yang, W.; Chen, X.; Zhang, X.; Zheng, L.; Liu, F., Flow and heat transfer of viscoelastic fluid with a novel space distributed-order constitution relationship, Comput. Math. Appl., 94, 94-103 (2021) · Zbl 1524.76021 · doi:10.1016/j.camwa.2021.04.023 |
[42] |
Yang, Z.; Zhang, J.; Niu, Y., Finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays, J. Appl. Math. Comput., 63, 1, 501-522 (2020) · Zbl 1475.34042 · doi:10.1007/s12190-020-01327-6 |
[43] |
Zaky, MA; Machado, JT, On the formulation and numerical simulation of distributed-order fractional optimal control problems, Commun. Nonlinear Sci. Numer. Simul., 52, 177-189 (2017) · Zbl 1510.49018 · doi:10.1016/j.cnsns.2017.04.026 |
[44] |
Želi, V.; Zorica, D., Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law, Phys. A, 492, 2316-2335 (2018) · Zbl 1514.80002 · doi:10.1016/j.physa.2017.11.150 |
[45] |
Zhou, F.; Zhao, Y.; Li, Y.; Chen, Y., Design, implementation and application of distributed order pi control, ISA Trans., 52, 3, 429-437 (2013) · doi:10.1016/j.isatra.2012.12.004 |