Numerical solution of nonlinear 2D optimal control problems generated by Atangana-Riemann-Liouville fractal-fractional derivative

Applied Numerical Mathematics - Tập 150 - Trang 507-518 - 2020
M.H. Heydari1
1Department of Mathematics, Shiraz university of Technology, Shiraz, Iran

Tài liệu tham khảo

Agrawal, 2008, A general finite element formulation for fractional variational problems, J. Math. Anal. Appl., 337, 1, 10.1016/j.jmaa.2007.03.105 Atangana, 2016, Derivative with two fractional orders: a new avenue of investigation toward revolution in fractional calculus, Eur. Phys. J. Plus, 131, 373, 10.1140/epjp/i2016-16373-2 Atangana, 2017, Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system, Chaos Solitons Fractals, 102, 396, 10.1016/j.chaos.2017.04.027 Atangana, 2018, Blind in a commutative world: simple illustrations with functions and chaotic attractors, Chaos Solitons Fractals, 114, 347, 10.1016/j.chaos.2018.07.022 Atangana, 2018, Non validity of index law in fractional calculus: a fractional differential operator with Markovian and non-Markovian properties, Phys. A, Stat. Mech. Appl., 505, 688, 10.1016/j.physa.2018.03.056 Atangana, 2019, Modeling attractors of chaotic dynamical systems with fractal-fractional operators, Chaos Solitons Fractals, 123, 320, 10.1016/j.chaos.2019.04.020 Bagley, 1985, Fractional calculus in the transient analysis of viscoelastically damped structures, AIAA J., 23, 918, 10.2514/3.9007 Baleanu, 2012, 10.1142/8180 Bhrawy, 2016, A new Legendre operational technique for delay fractional optimal control problems, Calcolo, 53, 521, 10.1007/s10092-015-0160-1 Canuto, 1988 Chelyshkov, 2006, Alternative orthogonal polynomials and quadratures, Electron. Trans. Numer. Anal., 25, 17 Dahaghin, 2017, A new optimization method for a class of time fractional convection-diffusion-wave equations with variable coefficients, Eur. Phys. J. Plus, 133, 130, 10.1140/epjp/i2017-11407-y Diethelm, 2002, Analysis of fractional differential equations, J. Math. Anal. Appl., 265, 229, 10.1006/jmaa.2000.7194 Engheta, 1996, On fractional calculus and fractional multipoles in electromagnetism, Antennas Propag., 44, 554, 10.1109/8.489308 Hassani, 2019, Numerical solution of fractional variational problems depending on indefinite integrals using transcendental Bernstein series, J. Vib. Control, 25, 1930, 10.1177/1077546319840901 Hassani, 2019, Solving two-dimensional variable-order fractional optimal control problems with transcendental Bernstein series, J. Comput. Nonlinear Dyn., 14 Hassani, 2019, Generalized shifted Chebyshev polynomials for fractional optimal control problems, Commun. Nonlinear Sci. Numer. Simul., 75, 50, 10.1016/j.cnsns.2019.03.013 Heydari, 2019, Chebyshev cardinal wavelets for nonlinear variable-order fractional quadratic integral equations, Appl. Numer. Math., 144, 190, 10.1016/j.apnum.2019.04.019 Heydari, 2018, A computational method for solving two-dimensional nonlinear variable-order fractional optimal control problems, Asian J. Control, 10.1002/asjc.1986 Heydari, 2014, An efficient computational method for solving fractional biharmonic equation, Comput. Math. Appl., 68, 269, 10.1016/j.camwa.2014.06.001 Heydari, 2016, Numerical solution of fractional sub-diffusion and time-fractional diffusion-wave equations via fractional-order Legendre functions, Eur. Phys. J. Plus, 131, 268, 10.1140/epjp/i2016-16268-2 Heydari, 2016, An efficient computational method based on the hat functions for solving fractional optimal control problems, Tbil. Math. J., 9, 143, 10.1515/tmj-2016-0007 Heydari, 2018, Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion, Commun. Nonlinear Sci. Numer. Simul., 64, 98, 10.1016/j.cnsns.2018.04.018 Heydari, 2019, Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion, Chaos Solitons Fractals, 124, 105, 10.1016/j.chaos.2019.04.040 Kulish, 2002, Application of fractional calculus to fluid mechanics, J. Fluids Eng., 124, 803, 10.1115/1.1478062 Langlands, 2005, The accuracy and stability of an implicit solution method for the fractional diffusion equation, J. Comput. Phys., 205, 719, 10.1016/j.jcp.2004.11.025 Lederman, 2004, Mathematical justification of a nonlinear integrodifferential equation for the propagation of spherical flames, Ann. Mat. Pura Appl., 183, 173, 10.1007/s10231-003-0085-1 Mohammadi, 2019, Numerical solution of two-dimensional variable-order fractional optimal control problem by generalized polynomial basis, J. Optim. Theory Appl., 180, 536, 10.1007/s10957-018-1389-z Moradi, 2019, A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets, J. Vib. Control, 25, 310, 10.1177/1077546318777338 Nemati, 2019, The use of the Ritz method and Laplace transform for solving 2d fractional-order optimal control problems described by the Roesser model, Asian J. Control, 21, 1189, 10.1002/asjc.1791 Oğuz, 2015, Chelyshkov collocation method for a class of mixed functional integro-differential equations, Appl. Math. Comput., 259, 943 Podlubny, 1999 Rahimkhani, 2019, Generalized fractional-order Bernoulli-Legendre functions: an effective tool for solving two-dimensional fractional optimal control problems, IMA J. Math. Control Inf., 36, 185, 10.1093/imamci/dnx041 Soltani Sarvestani, 2019, A wavelet approach for the multi-term time fractional diffusion-wave equation, Int. J. Comput. Math., 96, 640, 10.1080/00207160.2018.1458097 Yuste, 2006, Weighted average finite difference methods for fractional diffusion equations, J. Comput. Phys., 216, 264, 10.1016/j.jcp.2005.12.006 Zaky, 2018, A Legendre collocation method for distributed-order fractional optimal control problems, Nonlinear Dyn., 91, 2667, 10.1007/s11071-017-4038-4