[1] Abbas, S. and Mehdi, D. A new operational matrix for solving fractional order differential equations, Comput. Math. Appl. 59 (2010), 1326–1336.
[2] Adesanya, A.O., Yahaya, Y.A. Ahmed, B. and Onsachi, R.O. Numer-ical solution of linear integral and integro-differential equations using Boubakar collocation method, Inter. J. Math. Anal. Optim. Theory Appl. 2 (2019), 592–598.
[3] Ahmed, A.H., Kirtiwant, P.G. and Shakir, M.A. The approximate solu-tions of fractional integro-differential equations by using modified ado-mian decomposition method, Khayyam J. Math. 5 (1) (2019), 21-39.
[4] Ajileye, G. and Aminu, F.A. A numerical method using collocation ap-proach for the solution of Volterra-Fredholm integro-differential equa-tions, African Scientific Reports 1 (2022), 205–211.
[5] Ajileye, G. and Aminu, F.A. Approximate solution to first-order integro-differential equations using polynomial collocation approach, J. Appl. Computat Math. 11 (2022), 486.
[6] Ajileye, G. Amoo, S.A. and Ogwumu, O.D. Hybrid block method al-gorithms for solution of first order initial value problems in ordinary differential equations, J. Appl. Comput. Math. 7(2018) 390.
[7] Ajileye, G., James, A.A., Ayinde, A.M. and Oyedepo, T. Collocation approach for the computational solution of Fredholm-Volterra fractional order of integro-differential equations, J. Nig. Soc. Phys. Sci. 4 (2022), 834.
[8] Atabakan, Z.P., Nasab, A.K., Kiliçman, A. and Eshkuvatov, Z.K. Nu-merical solution of nonlinear Fredholm integro-differential equations us-ing spectral homotopy analysis method, Math. Probl. Eng. 9 (7) (2013) 674364.
[9] Berinde, V. Iterative approximation of fixed points, Romania. Editura Efemeride, Baia Mare, 2002.
[10] Bhraway, A.H. Tohidi, E. and Soleymani, F. A new Bernoulli matrix method for solving high order linear and nonlinear Fredholm integro-differential equations with piecewise interval, Appl. Math. Comput. 219 (2012), 482–497.
[11] Biazar, J. and Gholami, P.M. Application of variational iteration method for linear and nonlinear integro-differential-difference equations, Int. Math. Forum5 (2010), 3335–3341.
[12] Darania, P. and Ebadian, A. A method for the numerical solution of the integro-differential equations, Appl. Math. Comput. 188 (2007), 657–668.
[13] Elmaci, D. and Baykus Savasaneril, N. The Lucas Polynomial solution of linear Volterra-Fredholm integral equations, Matrix Sci. Math. 6(1) (2022), 21–25.
[14] Elmaci, D. and Baykus Savasaneril, N. Solutions of high-order linear Volterra integro-differential equations via Lucas polynomials, Montes Taurus J. Pure Appl. Math. 5 (1) (2023), 22–33.
[15] Ercan, C. and Kharerah, T. Solving a class of Volterra integral system by the differential transform method, Int. J. Nonlinear Sci. 16 (2013), 87–91.
[16] Gulsu, M. and Ozturk, Y. On the numerical solution of linear Fredholm-Volterra integro-differential Difference Equations with Piecewise Inter-vals, Appl. Appl. Math. Comput. 7(3) (2012), 556–557.
[17] James A.A. and Ajileye, G., Ayinde A.M. and Dunama, W. Hybrid-block method for the solution of second order non-linear differential equations, J. Adv. Math. Comput. Sci. 37(12) (2022), 156–169.2456-9968.
[18] Karakoc, S.B.G., Eryilmaz, A. and Basbuk, M. The approximate solu-tions of Fredholm integro-differential difference equations with variable coefficients via homotopy analysis method, Math. Probl. Eng. (2013) Article ID: 261645.
[19] Khan, R.H. and Bakodah, H.O. Adomian decomposition method and its modification for nonlinear Abel’s integral equations, Comput. Math. Appl. 7 (2013), 2349–2358.
[20] Matar, M.M. Nonlocal integro-differential equations with arbitrary frac-tional order, Konuralp J. Math. 4(1) (2016), 114–121.
[21] Mehdiyeva, G. Ibrahimov, V. and Imanova, M. On the construction of the multistep methods to solving the initial-value problem for ODE and the Volterra integro-differential equations, IAPE, Oxford, United Kingdom, 2019.
[22] Oyedepo, T., Ayinde, M.A., Adenipekun, A.E. and Ajileye, G. Least-squares collocation Bernstein method for solving system of linear frac-tional integro-differential equations, Int. J. Comput. Appl. 183(22) (2021), 0975–8887.
[23] Oyedepo, T., Ayoade, A.A. Ajileye, G. and Ikechukwu, N. J. Legen-dre computational algorithm for linear integro-differential equations, Cumhuriyet Science Journal 44(3) (2023), 561-566.
[24] Oyedepo, T., Ishola, C.Y., Ayoade, A.A. and Ajileye, G. Collocation computational algorithm for Volterra-Fredholm integro-differential equa-tions, Electron. J. Math. Anal. Appl. 11(2) (2023), 1–9.
[25] Palais, R.S. A simple proof of the Banach contraction principle, J. Fixed Point Theory Appl. 2 (2007) 221–223.
[26] Rahmani, L., Rahimi, B. and Mordad, M. Numerical solution of Volterra-Fredholm integro-differential equation by block pulse functions and operational matrices, Gen. Math. Notes 4 (2) (2011), 7–48.
[27] Taiwo, O.A., Alimi, A.T. and Akanmu, M.A. Numerical solutions for linear Fredholm integro-differential difference equations with variable co-efficients by collocation methods, JEPER 1 (2) (2014), 175–185.
[28] Volterra, V. Theory of functionals and of integral and integro-differential equations, Dover Publications, 2005.
[29] Yalcinbas, S. and Akkaya, T. A numerical approach for solving linear integro-differential-difference equations with Boubaker polynomial bases, Ain Shams Eng. J. 3(2) (2012), 153–161.
[30] Zada, L., Al-Hamami, M., Nawaz, R., Jehanzeb, S., Morsy, A., Abdel-Aty, A. and Nisar, K.S. A new approach for solving Fredholm integro-differential equations. Inform. Sci. Lett. 10(3) (2021), 407–415.
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