References
- S. Abbasbandy and S. Elyas, Application of variational iteration method for system of nonlinear Volterra integro-differential equations, Math. Comput. Appl. 2(14) (2009), 147-158.
- G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135(2) (1988), 501-544. https://doi.org/10.1016/0022-247x(88)90170-9
- S. Alao, F. Akinboro1, F. Akinpelu and R. Oderinu, Numerical solution of integro-differential equation using Adomian decomposition and variational iteration methods, IOSR J. Math., 10(4) (2014), 18-22.
- M.A. Araghi and S.S. Behzadi, Solving nonlinear Volterra-Fredholm integro-differential equations using the modified Adomian decomposition method, Comput. Methods Appl. Math., 9 (2009), 321-331. https://doi.org/10.2478/cmam-2009-0020
- S. Behzadi, S. Abbasbandy, T. Allahviranloo and A. Yildirim, Application of homotopy analysis method for solving a class of nonlinear Volterra-Fredholm integro-differential equations, J. Appl. Anal. Comput., 2(2) (2012), 127-136.
- M. Bani Issa and A. Hamoud, Solving systems of Volterra integro-differential equations by using semi-analytical techniques, Technology Reports of Kansai University, 62(3) (2020), 685-690.
- F.S. Fadhel, A.O. Mezaal and S.H. Salih, Approximate solution of the linear mixed Volterra-Fredholm integro-differential equations of second kind by using variational iteration method, Al- Mustansiriyah J. Sci., 24(5) (2013), 137-146.
- M.A. Fariborzi Araghi and S.S. Behzadi, Solving nonlinear Volterra-Fredholm integral differential equations using the modified Adomian decomposition method, Comput. Methods Appl. Math., 9 (2009), 1-11.
- M. Ghasemi, M. kajani and E. Babolian, Application of He's Homotopy Perturbation Method to Nonlinear Integro differential Equations, Appl. Math. Comput., 188 (2007), 538-548. https://doi.org/10.1016/j.amc.2006.10.016
- J.H. He, Variational iteration method for autonomous ordinary differential system, Appl. Math. Comput., 114 (2000), 115-123. https://doi.org/10.1016/S0096-3003(99)00104-6
- J.H. He, A variational approach to nonlinear problems and its application, Mech. Appl., 20(1) (1998), 30-34.
- J.H. He and S.Q. Wang, Variational iteration method for solving integro-differential equations, Phys. Lett. A, 367 (2007), 188-191. https://doi.org/10.1016/j.physleta.2007.02.049
- A. Hamoud and K. Ghadle, Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations, J. Appl. Comput. Mech., 5(1) (2019), 58-69.
- A. Hamoud and K. Ghadle, The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Probl. Anal. Issues Anal., 7(25) (2018), 41-58.
- A. Hamoud, M. SH. Bani Issa and K. Ghadle, Existence and uniqueness results for nonlinear Volterra-Fredholm integro-differential equations, Nonlinear Funct. Anal. Appl., 23(4) (2018), 797-805 https://doi.org/10.22771/NFAA.2018.23.04.15
- A. Hamoud and K. Ghadle, Homotopy analysis method for the first order fuzzy Volterra-Fredholm integro-differential equations, Indonesian J.f Electrical Eng. Comput. Sci., 11(3) (2018), 857-867. https://doi.org/10.11591/ijeecs.v11.i3.pp857-867
- A. Hamoud and K. Ghadle, Modified Adomian decomposition method for solving fuzzy Volterra-Fredholm integral equation, J. Indian Math. Soc., 85(1-2) (2018), 53-69. https://doi.org/10.18311/jims/2018/16260
- A. Hamoud, K. Ghadle and S. Atshan, The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method, Khayyam J. Math., 5(1) (2019), 21-39.
- A. Hamoud and K. Ghadle, Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, J. Math Mdel., 6(1) (2018), 91-104.
- A. Hamoud, A. Azeez and K. Ghadle, A study of some iterative methods for solving fuzzy Volterra-Fredholm integral equations, Indonesian J. Electrical Eng. Comput. Sci., 11(3) (2018), 1228-1235. https://doi.org/10.11591/ijeecs.v11.i3.pp1228-1235
- A. Hamoud, K. Hussain and K. Ghadle, The reliable modified Laplace Adomian decomposition method to solve fractional Volterra-Fredholm integro differential equations, Dyn. Continuous, Disc. Impul. Sys. Series B: Appl. Algo., 26 (2019), 171-184.
- K. Hussain, A. Hamoud and N. Mohammed, Some new uniqueness results for fractional integro-differential equations, Nonlinear Funct. Anal. Appl., 24(4) (2019), 827-836.
- H. Han, Y. Liu, T. Lu and X. He, New algorithm for the system of nonlinear weakly singular Volterra integral equations of the second kind and integro-differential equations, J. Inform. Comput. Sci. 7 (2010), 1229-1235.
- S.A. Khuri, A Laplace decomposition algorithm applied to class of nonlinear differential equations, J. Math. Appl. 4 (2001), 141-155. https://doi.org/10.1155/S1110757X01000183
- R. Mittal and R. Nigam, Solution of fractional integro-differential equations by Adomian decomposition method, Int. J. Appl. Math. Mech. 4(2) (2008), 87-94.
- N. Ngarhasta, B. Some, K. Abbaoui, and Y. Cherruaul, New numerical study of Adomian method applied to a diffusion model, Kybernetes, 31 (2002), 61-75. https://doi.org/10.1108/03684920210413764
- S.B. Shadan, The use of iterative method to solve two-dimensional nonlinear Volterra-Fredholm integro-differential equations, J. Comm. Numer. Anal., (2012), 1-20.
- Y. Salih and S. Mehmet, The approximate solution of higher order linear Volterra-Fredholm integro-differential equations in term of Taylor polynomials, Appl. Math. Comput., 112 (2000), 291-308. https://doi.org/10.1016/S0096-3003(99)00059-4
- A.M. Wazwaz, The modified decomposition method for analytic treatment of nonlinear integral equations and systems of nonlinear integral equations, Int. J. Compu. Math., 82(9) (2005), 1107-1115. https://doi.org/10.1080/00207160500113041