[1] Abdelaty, A.M., Roshdy, M., Said, L.A. and Radwan, A. G. Numeri-cal simulations and FPGA implementations of fractional-order systems based on product integration rules, IEEE Access. 8 (2020), 102093–102105.
[2] Ahmed, S.A., Elzaki, T.M. and Hassan, A.A. Solution of integral dif-ferential equations by new double integral transform (Laplace–Sumudu transform), Abstr. Appl. Anal. (2020), Art. ID 4725150, 7.
[3] Al-Ahmad, S., Sulaiman, I.M. and Mamat, M. An efficient modifica-tion of differential transform method for solving integral and integro-differential equations, Aust. J. Math. Anal. Appl. 17(2) (2020), Art. 5, 15.
[4] Amin, R., Shah, K., Asif, M., Khan, I. and Ullah, F. An efficient algo-rithm for numerical solution of fractional integro-differential equations via Haar wavelet, J. Comput. Appl. Math. 381(113028) (2021), 17.
[5] Arsalan Sajjadi, S., Saberi Najafi, H. and Aminikhah, H. A numerical study on the non‐smooth solutions of the nonlinear weakly singular frac-tional Volterra integro‐differential equations, Math. Methods Appl. Sci. 46(4) (2023), 4070–4084.
[6] Babolian, E. and Mordad, M. A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions, Comput. Math. Appl. 62(1) (2011), 187–198.
[7] Behera, S. and Ray, S. Saha. An efficient numerical method based on Euler wavelets for solving fractional order pantograph Volterra delay-integro-differential equations, J. Comput. Appl. Math. 406(113825) (2022), 23.
[8] Behera, S. and Ray, S. Saha. On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels, Comput. Appl. Math. 41(5) (2022), 1–32.
[9] Biazar, J. Solution of systems of integral–differential equations by Ado-mian decomposition method, Appl. Math. Comput. 168(2) (2005), 1232–1238.
[10] Biazar, J. and Ebrahimi, H. Orthonormal Bernstein polynomials for Volterra integral equations of the second kind, Int. J. Appl. Math. Res. 9(1) (2019), 9–20.
[11] Biazar, J. and Ebrahimi, H. A numerical algorithm for a class of non-linear fractional Volterra integral equations via modified hat functions, J. Integral Equ. Appl. 34(3) (2022), 295–316.
[12] Biazar, J. and Montazeri, R. Optimal homotopy asymptotic and multi-stage optimal homotopy asymptotic methods for solving system of volterra integral equations of the second kind, J. Appl. Math. 2019 (2019), Art. ID 3037273, 17.
[13] Derakhshan, M. A numerical scheme based on the Chebyshev functions to find approximate solutions of the coupled nonlinear sine-Gordon equa-tions with fractional variable orders, Abstr. Appl. Anal. 2021 (2021), Art. ID 8830727, 20.
[14] Du, H., Chen, Z. and Yang, T. A stable least residue method in repro-ducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel, Appl. Numer. Math. 157 (2020), 210–222.
[15] Hashemi Mehne, S.H. Differential transform method: A comprehensive review and analysis, Iranian Journal of Numerical Analysis and Opti-mization 12(3) (Special Issue), (2022), 629–657.
[16] Kukreja, V. K. An improvised collocation algorithm with specific end con-ditions for solving modified Burgers equation, Numer. Methods Partial Differ. Equ. 37(1) (2021), 874–896.
[17] Kythe, P.K. and Puri, P. Computational methods for linear integral equations, Birkhäuser Boston, Inc., Boston, MA, 2002.
[18] Leitman, M.J. An integro-differential equation for plane waves propa-gating into a random fluid: asymptotic behavior, SIAM J. Math. Anal. 12(4) (1981), 560–571.
[19] Mirzaee, F. and Hadadiyan, E. Numerical solution of Volterra–Fredholm integral equations via modification of hat functions, Appl. Math. Com-put. 280 (2016), 110–123.
[20] Moosavi Noori, S.R. and Taghizadeh, N. Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays, Adv. Differ. Equ. 2020(1) (2020), 1–25.
[21] Ndiaye, A. and Mansal, F. Existence and uniqueness results of Volterra-Fredholm integro-differential equations via Caputo fractional derivative, J. Math. (2021), Art. ID 5623388, 8.
[22] Nemati, S. and Lima, P M. Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modifi-cation of hat functions, Appl. Math. Comput. 327 (2018), 79–92.
[23] Özaltun, G., Konuralp, A. and Gümgüm, S. Gegenbauer wavelet solu-tions of fractional integro-differential equations, J. Comput. Appl. Math. 420(114830) (2023), 11.
[24] Podlubny, I. Fractional differential equations, Math. Sci. Eng. 198 (1999), Academic Press.
[25] Qiao L. and Xu, D. A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation, Adv. Comput. Math. 47(5) (2021), 1–22.
[26] Quentin, R., King, J.R., Sallard, E., Fishman, N., Thompson, R., Buch E.R. and Cohen, L.G. Differential brain mechanisms of selection and maintenance of information during working memory J. Neurosci. 39(19) (2019), 3728–3740.
[27] Rabbath, C.A. and Corriveau, D. A comparison of piecewise cubic Her-mite interpolating polynomials, cubic splines and piecewise linear func-tions for the approximation of projectile aerodynamics, Defence Tech-nology 15(5) (2019), 741–757.
[28] Rakshit G. and Rane, A.S. Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green’s kernel, J. Integral Equ. Appl. 32(4) (2020), 495–507.
[29] Riahi Beni, M. Legendre wavelet method combined with the Gauss quadra-ture rule for numerical solution of fractional integro-differential equa-tions, Iranian Journal of Numerical Analysis and Optimization 12(1) (2022), 229–249.
[30] Sabatier, J., Aoun, M., Oustaloup, A., Gregoire, G., Ragot, F. and Roy, P. Fractional system identification for lead acid battery state of charge estimation, Signal Process 86(10) (2006), 2645–2657.
[31] Vinagre, B.M. ,Monje, C.A. ,Calderón A.J. and Suárez, J.I. Fractional PID controllers for industry application. A brief introduction, J. Vib. Control, 13(9-10) (2007), 1419–1429.
[32] Wang, Y. and Zhu, Li. SCW method for solving the fractional integro-differential equations with a weakly singular kernel, Appl. Math. Comput. 275 (2022), 72–80.
[33] Xie, J., Wang, T., Ren, Z., Zhang J. and Quan, L. Haar wavelet method for approximating the solution of a coupled system of fractional-order integral–differential equations, Math. Comput. Simul 163 (2019), 80–89.
[34] Yang, Z. Gröbner Bases for Solving Multivariate Polynomial Equations, Computing Equilibria and Fixed Points: The Solution of Nonlinear In-equalities (1999) 265–288.
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