[1] H. Alrabaiah, I. Ahmad, R. Amin and K. Shah, “A numerical method for fractional variable order pantograph differential equations based on Haar wavelet,” Eng. Comput., 38 (2022) 2655-2668.
[2] J. António Tenreiro Machado and B. Parsa Moghaddam, “A robust algorithm for nonlinear variable-order fractional control systems with delay,” Int. J. Nonlinear Sci. Numer. Simul., 19 (3-4) (2018) 231-238.
[3] M. Alipour and S. Soradi Zeid, “Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method,” Comput. Methods Differ. Equ., 11(1) (2023) 52-64.
[4] R. Almeida, D. Tavares and D.F. Torres, “The VariableOrder Fractional Calculus of Variations,” Cham, Switzerland: Springer International Publishing, 2019.
[5] S. Ahmed, S. Jahan, K. Shah and T. Abdeljawad, “On computational analysis via fibonacci wavelet method for investigating some physical problems,” J. Appl. Math. Comput., 71(1) (2025) 531-550.
[6] M. Alipour, M.A. Vali, “Approximate optimal control of Volterra-Fredholm integral equations based on parametrization and variational iteration method,” Math. Commun. 26 (2021) 107-119.
[7] M. Alipour, M.A. Vali, A.H. Borzabadi, “A direct approach for approximate optimal control of integro-differential equations based on homotopy analysis and parametrization method,” IMA J. Math. Control. Inf. 34 (2) (2017) 611-630.
[8] M. Bilal, A. Ghafoor, M. Hussain, K. Shah and T. Abdeljawad, “Numerical Scheme for the Computational Study of Two Dimensional Diffusion and Burgers’ Systems with Stability and Error Estimate,” J. Nonlinear Math. Phys., 32(1 (2025) 1-23.
[9] A. H. Borzabadi, M. Azizsefat, “Numerically solution of optimal control problems governed by integro-differential equation via a hybrid iterative scheme,” WASJ, 10 (2010) 538-543.
[10] H. Dehestani and Y. Ordokhani, “A numerical study on fractional optimal control problems described by CaputoFabrizio fractional integro-differential equation,” Optim. Control. Appl. Methods., 44(4) (2023) 1873-1892.
[11] M. Du, Z. Wang and H. Hu, “Measuring memory with the order of fractional derivative,” Sci. Rep., 3 (1) (2013) 3431.
[12] G. Dewangan, A. Singh and A. Kanaujiya, “Generalized distributed-order fractional optimal control problem using Laguerre wavelet method,” J. Math. Modell., (2025) 707-725.
[13] G. Ghanbari and M. Razzaghi, “Numerical solutions for distributed-order fractional optimal control problems by using generalized fractional-order Chebyshev wavelets,” Nonlinear Dyn., 108(1) (2022) 265-277.
[14] M.H. Heydari and Z. Avazzadeh, “ A direct computational method for nonlinear variable-order fractional delay optimal control problems,” Asian J. Control., 23 (6) (2021) 2709-2718.
[15] H. Hassani and Z. Avazzadeh, ”Transcendental Bernstein series for solving nonlinear variable order fractional optimal control problems,” Appl. Math. Comput., 362 (2019) 124563.
[16] H. Hassani, Z. Avazzadeh and J.A.T. Machado, “Solving two-dimensional variable-order fractional optimal control problems with transcendental Bernstein series,” J. Comput. Nonlinear Dyn., 14 (6) (2019) 061001.
[17] M.H. Heydari, M. Razzaghi and Z. Avazzadehm, “Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations,” J. Vib. Control., 29 (5-6) (2023) 1164-1175.
[18] M. Izadi and H. M. Srivastava, “A novel matrix technique for multi-order pantograph differential equations of fractional order,” Proc. R. Soc. A, 477(2253) (2021) 20210321.
[19] A. Keimer and L. Pflug, “Modeling infectious diseases using integro-differential equations: Optimal control strategies for policy decisions and Applications in COVID19," Res Gate., (2020) 10.13140/RG.2.2.10845.44000.
[20] R. Khanduzi, A. Ebrahimzadeh and S.P.A. Beik, “Optimal control of fractional integro-differential systems based on a spectral method and grey wolf optimizer,” Int. J. Optim. Control: Theor. Appl., (IJOCTA). 10 (1) (2020) 55-65.
[21] K. Maleknejad and A. Ebrahimzadeh, “The use of rationalized Haar wavelet collocation method for solving optimal control of Volterra integral equations,” J. Vib. Control., 21 (2015) 1958-1967.
[22] F. Mirzaee, E. Hadadiya, “Numerical solution of optimal control problem of the non-linear Volterra integral equations via generalized hat functions,” IMA J. Math. Control Inf. 34(3) (2017) 889-904.
[23] M. Michalska and J. Szynal, “A new bound for the Laguerre polynomials,” J. Comput. Appl. Math., 133 (1-2) (2001) 489-493.
[24] S.S. Ray and S. Behera, ‘Two-dimensional wavelets operational method for solving Volterra weakly singular partial integro-differential equations,” J. Comput. Appl. Math., 366 (2020) 112411.
[25] N. Sweilam, S. Mahyoub Al-Mekhlafi, O. Albalawi and J. Tenreiro Machado, “Optimal control of variable-order fractional model for delay cancer,” App. Math. Modell., 89 (2021) 1557-1574.
[26] S. Soradi-Zeid, H. Jahanshahi, A. Yousefpour and S. Bekiros, “King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems,” Chaos Solit. Fract., 132 (2020) 109569.
[27] S. Sabermahani, Y. Ordokhani, K. Rabiei and M. Razzaghi, “Solution of optimal control problems governed by volterra integral and fractional integro-differential equations,” J. Vib. Control., 29(15-16) (2023) 3796-3808.
[28] S. Sabermahani and Y. Ordokhani, “Solving distributedorder fractional optimal control problems via the Fibonacci wavelet method,” J. Vib. Control, 30(1-2) (2024), 418-432.
[29] S. Sabermahani, Y. Ordokhani and P. Rahimkhani, “Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems,” Chaos Solit. Fract., 170 (2023) 113348.
[30] S. Soradi-Zeid and M. Alipour, “A collocation method using generalized Laguerre polynomials for solving nonlinear optimal control problems governed by integrodifferential equations,” J. Comput. Appl. Math., 436 (2024) 115410.
[31] K. Shah, M. Sarwar and T. Abdeljawad, “Modeling Virus Mutation Dynamics Using Piecewise Fractional Derivatives,” Eur. J. Pure Appl. Math., 18(2) (2025) 6053-6053.
[32] A. Singh, A. Kanaujiya and J. Mohapatra, “Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem,” J. Appl. Math. Comput., 70(4) (2024) 3135-3160.
[33] A. Singh, A. Kanaujiya and J. Mohapatra, “Euler wavelets method for optimal control problems of fractional integrodifferential equations,” J. Comput. Appl. Math., 454 (2025) 116178.
[34] A. Singh, A. Kanaujiya and J. Mohapatra, “An efficient generalized Lucas wavelet operational matrix method for optimal control problems,” J. Comput. Appl. Math., (2025) 116749.
[35] F. Soufivand, F. Soltanian and K. Mamehrashi, “An operational matrix method based on the Gegenbauer polynomials for solving a class of fractional optimal control problems,” Int. J. Ind. Electron. Control Optim., 4(4) (2021) 475-484.
[36] E. Tohidi and O.R.N. Samadi, “Optimal control of nonlinear Volterra integral equations via Legendre polynomials,” IMA J. Math. Control Inf., 30(1) (2013) 67-83.
[37] C.A. Valentim, J.A. Rabi, S.A. David and J.A.T. Machado. “On multistep tumor growth models of fractional variableorder,” Biosystems, 199 (2021) 104294.
[38] Q. Yu, V. Vegh, F. Liu and I. Turner, “A variable order fractional differential-based texture enhancement algorithm with application in medical imaging,” PLOS ONE, 10(7) (2015) e0132952.
[39] X. Zheng, H. Wang, “A hidden-memory of variable-order time-fractional optimal control model: Analysis and approximation,” SIAM J. Control Optim., 59 (3) (2021) 1851-1880.
[40] S.S. Zeid, S, Effati and A.V. Kamyad, “Approximation methods for solving fractional optimal control problems,” Comput. Appl. Math., 37(2018) 158-182.
)