Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems
Summary In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented....
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| Published in | Optimal control applications & methods Vol. 41; no. 2; pp. 395 - 416 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Glasgow
Wiley Subscription Services, Inc
01.03.2020
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| Abstract | Summary
In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique. |
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| AbstractList | Summary
In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique. In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique. |
| Author | Yousefi, Sohrab‐Ali Ordokhani, Yadollah Sabermahani, Sedigheh |
| Author_xml | – sequence: 1 givenname: Sedigheh orcidid: 0000-0002-7320-8908 surname: Sabermahani fullname: Sabermahani, Sedigheh organization: Alzahra University – sequence: 2 givenname: Yadollah orcidid: 0000-0002-5167-6874 surname: Ordokhani fullname: Ordokhani, Yadollah email: ordokhani@alzahra.ac.ir organization: Alzahra University – sequence: 3 givenname: Sohrab‐Ali surname: Yousefi fullname: Yousefi, Sohrab‐Ali organization: Shahid Beheshti University |
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| Cites_doi | 10.1007/BF00933142 10.1016/j.chaos.2007.03.007 10.1016/S0377-0427(99)00390-8 10.1049/ip-d.1983.0051 10.1016/j.camwa.2011.04.024 10.2307/1938740 10.1016/S0006-3495(02)75249-1 10.1137/S0036139903434833 10.1177/1077546316687936 10.1016/j.asej.2013.11.007 10.1109/TAC.2005.861718 10.1016/j.proeng.2017.09.529 10.1002/mma.4463 10.1186/1029-242X-2013-205 10.1177/1077546305058662 10.1016/j.apm.2011.03.025 10.1007/978-3-540-30726-6 10.1016/j.matcom.2003.10.003 10.1155/2014/694580 10.1002/oca.843 10.1016/j.mbs.2005.12.006 10.1016/j.jtbi.2005.11.007 10.1007/s10957-011-9932-1 10.1007/s10957-009-9548-x 10.1186/1687-1847-2013-262 10.1038/344660a0 10.1016/j.jtice.2009.04.013 10.1002/oca.2163 10.1002/1099-1514(200005/06)21:3<91::AID-OCA669>3.0.CO;2-C 10.3934/jimo.2014.10.413 10.1016/j.cpc.2010.03.014 10.1007/s40314-014-0142-y 10.1155/S1024123X01001673 10.1016/j.sysconle.2015.04.013 10.1006/jmaa.1995.1239 10.1137/0316013 10.1177/1077546307087435 10.1002/oca.2351 10.1016/S0025-5564(99)00055-3 10.1177/1077546317727821 10.1093/imamci/dnu012 10.1007/s00285-003-0211-0 10.1177/1077546307087434 10.1007/s002850050194 10.1002/asjc.1371 10.1002/oca.2349 10.1016/j.apm.2015.09.072 10.1186/s40064-016-2853-6 10.1080/00207160801923056 10.1016/j.cnsns.2010.07.017 10.1016/j.apm.2017.08.025 10.1016/j.apm.2014.04.064 |
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| References | 2004; 65 2017; 40 2004; 64 2009; 86 2007; 184 2011; 62 2015; 32 2010; 181 2017; 199 1990; 344 2011; 16 2013; 6 2016; 37 2018; 39 1979; 29 2014; 5 2001; 130 2015; 82 2013; 2013 2002; 83 2003; 47 2000; 163 2006; 241 2016; 40 2006; 200 2014; 10 2006; 51 1983; 130 2000; 21 2008; 14 2006 2011; 35 1978; 16 2014; 2014 1995; 193 2010; 41 1992; 73 2018; 24 2016; 5 2012; 153 2009; 30 2001; 7 2017; 15 1999; 39 2009; 143 2014; 38 2019 2017; 19 2015 1998; 6 2012; 7 2018; 53 2005; 11 2014; 34 2009; 39 e_1_2_9_31_1 e_1_2_9_52_1 e_1_2_9_50_1 e_1_2_9_10_1 e_1_2_9_35_1 e_1_2_9_33_1 e_1_2_9_54_1 Wang XT (e_1_2_9_56_1) 2007; 184 Cooke K (e_1_2_9_4_1) 1998; 6 Sedaghat S (e_1_2_9_46_1) 2012; 7 e_1_2_9_14_1 e_1_2_9_39_1 e_1_2_9_37_1 e_1_2_9_58_1 e_1_2_9_41_1 e_1_2_9_20_1 Novotna V (e_1_2_9_12_1) 2013; 6 e_1_2_9_22_1 e_1_2_9_45_1 e_1_2_9_24_1 e_1_2_9_43_1 e_1_2_9_8_1 Göllmann L (e_1_2_9_26_1) 2014; 10 e_1_2_9_6_1 e_1_2_9_60_1 e_1_2_9_2_1 e_1_2_9_49_1 e_1_2_9_28_1 e_1_2_9_47_1 e_1_2_9_30_1 e_1_2_9_53_1 e_1_2_9_51_1 e_1_2_9_11_1 e_1_2_9_34_1 e_1_2_9_57_1 e_1_2_9_32_1 e_1_2_9_55_1 Sabermahani S (e_1_2_9_16_1) 2019 e_1_2_9_15_1 e_1_2_9_38_1 e_1_2_9_17_1 e_1_2_9_36_1 e_1_2_9_59_1 e_1_2_9_19_1 Sabermahani S (e_1_2_9_18_1) 2019 e_1_2_9_42_1 e_1_2_9_61_1 e_1_2_9_21_1 Düsünceli F (e_1_2_9_40_1) 2017; 15 e_1_2_9_23_1 e_1_2_9_44_1 e_1_2_9_7_1 e_1_2_9_5_1 e_1_2_9_3_1 Ha P (e_1_2_9_13_1) 2015 e_1_2_9_9_1 e_1_2_9_25_1 e_1_2_9_27_1 e_1_2_9_48_1 e_1_2_9_29_1 |
| References_xml | – volume: 64 start-page: 597 issue: 6 year: 2004 end-page: 607 article-title: Solution of time‐varying delay systems by hybrid functions publication-title: Math Comput Simul – volume: 39 start-page: 1005 year: 2009 end-page: 1019 article-title: On k‐Fibonacci sequences and polynomials and their derivatives publication-title: Chaos Solit Fractals – volume: 6 start-page: 321 issue: 4 year: 1998 end-page: 354 article-title: Analyses of an antiviral immune response model with time delays publication-title: Can Appl Math Q – volume: 30 start-page: 341 issue: 4 year: 2009 end-page: 365 article-title: Optimal control problems with delays in state and control variables subject to mixed control–state constraints publication-title: Optim Control Appl Meth – volume: 37 start-page: 190 issue: 1 year: 2016 end-page: 211 article-title: Optimal control of linear multi‐delay systems based on a multi‐interval decomposition scheme publication-title: Optim Control Appl Meth – volume: 39 start-page: 302 issue: 1 year: 2018 end-page: 325 article-title: A novel approach for the numerical investigation of optimal control problems containing multiple delays publication-title: Optim Control Appl Meth – volume: 10 start-page: 413 issue: 2 year: 2014 end-page: 441 article-title: Theory and applications of optimal control problems with multiple time‐delays publication-title: J Ind Manag Optim – volume: 62 start-page: 1038 issue: 3 year: 2011 end-page: 1045 article-title: Application of Legendre wavelets for solving fractional differential equations publication-title: Comput Math Appl – volume: 32 start-page: 623 issue: 3 year: 2015 end-page: 638 article-title: Numerical solution of the time‐delayed optimal control problems with hybrid functions publication-title: IMA J Math Control Inf – volume: 51 start-page: 91 issue: 1 year: 2006 end-page: 97 article-title: Optimal control for linear systems with multiple time delays in control input publication-title: IEEE Trans Autom Control – volume: 199 start-page: 2772 year: 2017 end-page: 2777 article-title: Active vibration control of lightweight floor systems publication-title: Procedia Engineering – volume: 16 start-page: 1216 issue: 3 year: 2011 end-page: 1226 article-title: Numerical solution of nonlinear Volterra integro‐differential equations of arbitrary order by CAS wavelets publication-title: Commun Nonlinear Sci Numer Simul – volume: 130 start-page: 300 issue: 6 year: 1983 end-page: 312 article-title: Optimal control of linear systems with delays in state and control via Walsh functions publication-title: IEE Proc D Control Theory Appl – volume: 2013 start-page: 205 issue: 1 year: 2013 article-title: Several identities involving the Fibonacci polynomials and Lucas polynomials publication-title: J Inequalities Appl – volume: 40 start-page: 2756 issue: 4 year: 2016 end-page: 2769 article-title: An efficient recursive shooting method for the optimal control of time‐varying systems with state time‐delay publication-title: Appl Math Model – volume: 83 start-page: 2349 issue: 5 year: 2002 end-page: 2359 article-title: A reduced model clarifies the role of feedback loops and time delays in the drosophila circadian oscillator publication-title: Biophysical Journal – volume: 241 start-page: 109 issue: 1 year: 2006 end-page: 119 article-title: An alternative formulation for a delayed logistic equation publication-title: J Theor Biol – volume: 7 start-page: 337 issue: 4 year: 2001 end-page: 353 article-title: A hybrid domain analysis for systems with delays in state and control publication-title: Math Probl Eng – volume: 39 start-page: 357 issue: 1 year: 2018 end-page: 376 article-title: Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets publication-title: Optim Control Appl Meth – volume: 47 start-page: 270 issue: 3 year: 2003 end-page: 294 article-title: A delay differential equation model for tumor growth publication-title: J Math Biol – volume: 86 start-page: 1572 issue: 9 year: 2009 end-page: 1590 article-title: A wavelet Petrov‐Galerkin method for solving integro‐differential equations publication-title: Int J Comput Math – volume: 40 start-page: 6389 issue: 18 year: 2017 end-page: 6410 article-title: Generalized Bessel functions: theory and their applications publication-title: Math Methods Appl Sci – volume: 5 start-page: 585 issue: 2 year: 2014 end-page: 594 article-title: A novel matrix approach to fractional finite difference for solving models based on nonlinear fractional delay differential equations publication-title: Ain Shams Eng J – volume: 15 start-page: 229 issue: 3 year: 2017 end-page: 238 article-title: Fibonacci matrix polynomial method for linear complex differential equations publication-title: Asian J Math Comput Res – volume: 14 start-page: 1499 issue: 9‐10 year: 2008 end-page: 1511 article-title: A fractional adaptation scheme for lateral control of an AGV publication-title: J Vib Control – volume: 163 start-page: 201 issue: 2 year: 2000 end-page: 215 article-title: A model of HIV‐1 pathogenesis that includes an intracellular delay publication-title: Mathematical Biosciences – volume: 130 start-page: 75 issue: 1‐2 year: 2001 end-page: 90 article-title: Numerical solution of time‐delayed functional differential equation control systems publication-title: J Comput Appl Math – volume: 200 start-page: 1 issue: 1 year: 2006 end-page: 27 article-title: Estimates of kinetic parameters from HIV patient data during primary infection through the eyes of three different models publication-title: Mathematical Biosciences – start-page: 1 year: 2019 end-page: 28 article-title: Fractional‐order general Lagrange scaling functions and their applications publication-title: BIT Numer Math – year: 2015 – volume: 2013 start-page: 262 issue: 1 year: 2013 article-title: A new Fibonacci type collocation procedure for boundary value problems publication-title: Adv Differ Equ – volume: 41 start-page: 54 issue: 1 year: 2010 end-page: 64 article-title: The solutions of time‐delayed optimal control problems by the use of modified line‐up competition algorithm publication-title: J Taiwan Inst Chem Eng – volume: 11 start-page: 1455 issue: 12 year: 2005 end-page: 1468 article-title: Analysis of time‐delay systems via hybrid of block‐pulse functions and Taylor series publication-title: J Vib Control – volume: 24 start-page: 4505 issue: 19 year: 2018 end-page: 4512 article-title: A new approach for the optimal control of time‐varying delay systems with external persistent matched disturbances publication-title: J Vib Control – volume: 181 start-page: 1255 issue: 7 year: 2010 end-page: 1265 article-title: Solution of a nonlinear time‐delay model in biology via semi‐analytical approaches publication-title: Comput Phys Commun – volume: 193 start-page: 329 issue: 1 year: 1995 end-page: 352 article-title: Global periodic solutions for a differential delay system modeling a microbial population in the chemostat publication-title: J Math Anal Appl – volume: 35 start-page: 5235 issue: 11 year: 2011 end-page: 5244 article-title: Numerical solution of time‐varying delay systems by Chebyshev wavelets publication-title: Appl Math Model – volume: 16 start-page: 169 issue: 2 year: 1978 end-page: 208 article-title: Hereditary control problems: numerical methods based on averaging approximations publication-title: SIAM J Control Optim – volume: 65 start-page: 316 issue: 1 year: 2004 end-page: 335 article-title: Delayed coupling between two neural network loops publication-title: SIAM J Appl Math – volume: 184 start-page: 849 issue: 2 year: 2007 end-page: 856 article-title: Numerical solutions of optimal control for time delay systems by hybrid of block‐pulse functions and Legendre polynomials publication-title: Appl Math Comput – volume: 38 start-page: 6038 issue: 24 year: 2014 end-page: 6051 article-title: Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations publication-title: Appl Math Model – volume: 39 start-page: 332 issue: 4 year: 1999 end-page: 352 article-title: Interaction of maturation delay and nonlinear birth in population and epidemic models publication-title: J Math Biol – volume: 7 start-page: 43 issue: 1 year: 2012 end-page: 57 article-title: Stability and numerical solution of time variant linear systems with delay in both the state and control publication-title: Iran J Math Sci Inform – volume: 153 start-page: 338 issue: 2 year: 2012 end-page: 356 article-title: Optimal control of delay systems by using a hybrid functions an approximation publication-title: J Optim Theory Appl – volume: 29 start-page: 383 issue: 3 year: 1979 end-page: 408 article-title: Approximation of nonlinear functional differential equation control systems publication-title: J Optim Theory Appl – volume: 19 start-page: 554 issue: 2 year: 2017 end-page: 563 article-title: An efficient finite difference method for the time‐delay optimal control problems with time‐varying delay publication-title: Asian J Control – volume: 21 start-page: 91 issue: 3 year: 2000 end-page: 105 article-title: Numerical solution of time‐delayed optimal control problems by iterative dynamic programming publication-title: Optim Control Appl Meth – volume: 5 start-page: 1375 issue: 1 year: 2016 article-title: Numerical solutions and error estimations for the space fractional diffusion equation with variable coefficients via Fibonacci collocation method publication-title: SpringerPlus – start-page: 1 year: 2019 end-page: 12 article-title: Fractional‐order Fibonacci‐hybrid functions approach for solving fractional delay differential equations publication-title: Eng w Comput – year: 2006 – volume: 14 start-page: 1487 issue: 9‐10 year: 2008 end-page: 1498 article-title: Analog fractional order controller in temperature and motor control applications publication-title: J Vib Control – volume: 2014 year: 2014 article-title: A matrix method based on the Fibonacci polynomials to the generalized pantograph equations with functional arguments publication-title: Adv Math Phys – volume: 82 start-page: 40 year: 2015 end-page: 50 article-title: An iterative method for suboptimal control of linear time‐delayed systems publication-title: Syst Control Lett – volume: 6 start-page: 77 issue: 10 year: 2013 end-page: 82 article-title: Application of delay differential equations in the model of the relationship between unemployment and inflation publication-title: Trends Econ Manag – volume: 53 start-page: 189 year: 2018 end-page: 213 article-title: A direct approach for the solution of nonlinear optimal control problems with multiple delays subject to mixed state‐control constraints publication-title: Appl Math Model – volume: 143 start-page: 107 issue: 1 year: 2009 end-page: 121 article-title: Optimal control of linear time‐delayed systems by linear Legendre multiwavelets publication-title: J Optim Theory Appl – volume: 344 start-page: 660 issue: 6267 year: 1990 end-page: 663 article-title: Rarity of density dependence or population regulation with lags publication-title: Nature – volume: 73 start-page: 289 issue: 1 year: 1992 end-page: 305 article-title: Complex dynamics in ecological time series publication-title: Ecology – volume: 34 start-page: 831 issue: 3 year: 2014 end-page: 846 article-title: An approximate method for numerically solving multi‐dimensional delay fractional optimal control problems by Bernstein polynomials publication-title: Comput Appl Math – volume: 24 start-page: 2430 issue: 12 year: 2018 end-page: 2446 article-title: Suboptimal control of fractional‐order dynamic systems with delay argument publication-title: J Vib Control – ident: e_1_2_9_60_1 doi: 10.1007/BF00933142 – ident: e_1_2_9_35_1 doi: 10.1016/j.chaos.2007.03.007 – ident: e_1_2_9_61_1 doi: 10.1016/S0377-0427(99)00390-8 – ident: e_1_2_9_52_1 doi: 10.1049/ip-d.1983.0051 – volume: 6 start-page: 77 issue: 10 year: 2013 ident: e_1_2_9_12_1 article-title: Application of delay differential equations in the model of the relationship between unemployment and inflation publication-title: Trends Econ Manag – ident: e_1_2_9_41_1 doi: 10.1016/j.camwa.2011.04.024 – ident: e_1_2_9_11_1 doi: 10.2307/1938740 – start-page: 1 year: 2019 ident: e_1_2_9_16_1 article-title: Fractional‐order general Lagrange scaling functions and their applications publication-title: BIT Numer Math – ident: e_1_2_9_6_1 doi: 10.1016/S0006-3495(02)75249-1 – ident: e_1_2_9_9_1 doi: 10.1137/S0036139903434833 – ident: e_1_2_9_22_1 doi: 10.1177/1077546316687936 – ident: e_1_2_9_50_1 doi: 10.1016/j.asej.2013.11.007 – ident: e_1_2_9_27_1 doi: 10.1109/TAC.2005.861718 – ident: e_1_2_9_53_1 doi: 10.1016/j.proeng.2017.09.529 – ident: e_1_2_9_30_1 doi: 10.1002/mma.4463 – volume: 184 start-page: 849 issue: 2 year: 2007 ident: e_1_2_9_56_1 article-title: Numerical solutions of optimal control for time delay systems by hybrid of block‐pulse functions and Legendre polynomials publication-title: Appl Math Comput – ident: e_1_2_9_36_1 doi: 10.1186/1029-242X-2013-205 – ident: e_1_2_9_17_1 doi: 10.1177/1077546305058662 – ident: e_1_2_9_44_1 doi: 10.1016/j.apm.2011.03.025 – volume: 7 start-page: 43 issue: 1 year: 2012 ident: e_1_2_9_46_1 article-title: Stability and numerical solution of time variant linear systems with delay in both the state and control publication-title: Iran J Math Sci Inform – ident: e_1_2_9_47_1 doi: 10.1007/978-3-540-30726-6 – ident: e_1_2_9_48_1 doi: 10.1016/j.matcom.2003.10.003 – volume-title: Analysis and Numerical Solutions of Delay Differential Algebraic Equations year: 2015 ident: e_1_2_9_13_1 – ident: e_1_2_9_38_1 doi: 10.1155/2014/694580 – ident: e_1_2_9_34_1 doi: 10.1002/oca.843 – ident: e_1_2_9_2_1 doi: 10.1016/j.mbs.2005.12.006 – ident: e_1_2_9_14_1 doi: 10.1016/j.jtbi.2005.11.007 – ident: e_1_2_9_25_1 doi: 10.1007/s10957-011-9932-1 – ident: e_1_2_9_28_1 doi: 10.1007/s10957-009-9548-x – ident: e_1_2_9_37_1 doi: 10.1186/1687-1847-2013-262 – ident: e_1_2_9_10_1 doi: 10.1038/344660a0 – ident: e_1_2_9_55_1 doi: 10.1016/j.jtice.2009.04.013 – volume: 15 start-page: 229 issue: 3 year: 2017 ident: e_1_2_9_40_1 article-title: Fibonacci matrix polynomial method for linear complex differential equations publication-title: Asian J Math Comput Res – ident: e_1_2_9_29_1 doi: 10.1002/oca.2163 – ident: e_1_2_9_31_1 doi: 10.1002/1099-1514(200005/06)21:3<91::AID-OCA669>3.0.CO;2-C – volume: 10 start-page: 413 issue: 2 year: 2014 ident: e_1_2_9_26_1 article-title: Theory and applications of optimal control problems with multiple time‐delays publication-title: J Ind Manag Optim doi: 10.3934/jimo.2014.10.413 – ident: e_1_2_9_49_1 doi: 10.1016/j.cpc.2010.03.014 – ident: e_1_2_9_59_1 doi: 10.1007/s40314-014-0142-y – ident: e_1_2_9_15_1 doi: 10.1155/S1024123X01001673 – ident: e_1_2_9_57_1 doi: 10.1016/j.sysconle.2015.04.013 – ident: e_1_2_9_5_1 doi: 10.1006/jmaa.1995.1239 – ident: e_1_2_9_51_1 doi: 10.1137/0316013 – ident: e_1_2_9_19_1 doi: 10.1177/1077546307087435 – ident: e_1_2_9_21_1 doi: 10.1002/oca.2351 – ident: e_1_2_9_3_1 doi: 10.1016/S0025-5564(99)00055-3 – ident: e_1_2_9_33_1 doi: 10.1177/1077546317727821 – ident: e_1_2_9_54_1 doi: 10.1093/imamci/dnu012 – ident: e_1_2_9_8_1 doi: 10.1007/s00285-003-0211-0 – ident: e_1_2_9_20_1 doi: 10.1177/1077546307087434 – ident: e_1_2_9_7_1 doi: 10.1007/s002850050194 – start-page: 1 year: 2019 ident: e_1_2_9_18_1 article-title: Fractional‐order Fibonacci‐hybrid functions approach for solving fractional delay differential equations publication-title: Eng w Comput – volume: 6 start-page: 321 issue: 4 year: 1998 ident: e_1_2_9_4_1 article-title: Analyses of an antiviral immune response model with time delays publication-title: Can Appl Math Q – ident: e_1_2_9_58_1 doi: 10.1002/asjc.1371 – ident: e_1_2_9_24_1 doi: 10.1002/oca.2349 – ident: e_1_2_9_32_1 doi: 10.1016/j.apm.2015.09.072 – ident: e_1_2_9_39_1 doi: 10.1186/s40064-016-2853-6 – ident: e_1_2_9_45_1 doi: 10.1080/00207160801923056 – ident: e_1_2_9_43_1 doi: 10.1016/j.cnsns.2010.07.017 – ident: e_1_2_9_23_1 doi: 10.1016/j.apm.2017.08.025 – ident: e_1_2_9_42_1 doi: 10.1016/j.apm.2014.04.064 |
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In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed.... In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This... |
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| SubjectTerms | Delay Fibonacci wavelets Galerkin method Initial conditions Iterative methods Numerical methods numerical solution operational matrix Optimal control time‐varying delay problem Wavelet analysis |
| Title | Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems |
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