References
- M.A. Araghi and S.S. Behzadi, Solving nonlinear Volterra-Fredholm integro-differential equations using the modified Adomian decomposition method, Comput. Methods in Appl. Math., 9 (2009), 321-331. https://doi.org/10.2478/cmam-2009-0020
- S.H. Behiry and S.I. Mohamed, Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method, Natural Science, 4 (2012), no. 8, 581-587. https://doi.org/10.4236/ns.2012.48077
- E. Babolian, Z. Masouri, and S. Hatamzadeh, New direct method to solve nonlinear Volterra-Fredholm integral and integro differential equation using operational matrix with Block-Pulse functions, Progress in Electromagnetic Research, B 8 (2008), 59-76.
- S.M. El-Sayed, D. Kaya, and S. Zarea, The decomposition method applied to solve high-order linear Volterra-Fredholm integro-differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 5 (2004), no. 2, 105-112.
- 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 (2013), no. 5, 137-146.
- 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 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.A. Hamoud and K.P. Ghadle, Existence and uniqueness of the solution for Volterra-Fredholm integro-differential equations, Journal of Siberian Federal University. Mathematics & Physics, 11 (2018), no. 6, 692-701. https://doi.org/10.17516/1997-1397-2018-11-6-692-701
- A.A. Hamoud and K.P. Ghadle, Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, Journal of Mathematical Modeling, 6 (2018), no. 1, 91-104.
- A.A. Hamoud and K.P. Ghadle, Homotopy analysis method for the first order fuzzy Volterra-Fredholm integro-differential equations, Indonesian J. Elec. Eng. & Comp. Sci., 11 (2018), no. 3, 857-867. https://doi.org/10.11591/ijeecs.v11.i3.pp857-867
- A.A. Hamoud and K.P. Ghadle, Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations, J. Appl. Comp. Mech., 5 (2019), no. 1, 58-69.
- A.A. Hamoud and K.P. Ghadle, Existence and uniqueness of solutions for fractional mixed Volterra-Fredholm integro-differential equations, Indian J. Math., 60 (2018), no. 3, 375-395.
- A.A. Hamoud and K.P. Ghadle, The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Probl. Anal. Issues Anal., 7(25) (2018), no. 1, 41-58.
- A.A. Hamoud, K.P. Ghadle, and S.M. Atshan, The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method, Khayyam Journal of Mathematics, 5 (2019), no. 1, 21-39.
- A.A. Hamoud and K.P. Ghadle, The reliable modified of Laplace Adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equations, Korean J. Math., 25 (2017), no. 3, 323-334. https://doi.org/10.11568/kjm.2017.25.3.323
- A.A. Hamoud, L.A. Dawood, K.P. Ghadle, and S.M. Atshan, Usage of the modified variational iteration technique for solving Fredholm integro-differential equations, International Journal of Mechanical and Production Engineering Research and Development, 9 (2019), no. 2, 895-902. https://doi.org/10.24247/ijmperdapr201987
- A.A. Hamoud, K.H. Hussain, and K.P. Ghadle, The reliable modified Laplace Adomian decomposition method to solve fractional Volterra-Fredholm integro-differential equations, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 26 (2019), 171-184.
- A.A. Hamoud and K.P. Ghadle, Modified Adomian decomposition method for solving fuzzy Volterra-Fredholm integral equations, J. Indian Math. Soc., 85 (2018), no. 1-2, 52-69.
- A.A. Hamoud and K.P. Ghadle, M. Bani Issa, Giniswamy, Existence and uniqueness theorems for fractional Volterra-Fredholm integro-differential equations, Int. J. Appl. Math., 31 (2018), no. 3, 333-348.
- A.A. Hamoud, A.D. Azeez, and K.P. Ghadle, A study of some iterative methods for solving fuzzy Volterra-Fredholm integral equations, Indonesian J. Elec. Eng. & Comp. Sci., 11 (2018), no. 3, 1228-1235. https://doi.org/10.11591/ijeecs.v11.i3.pp1228-1235
- A.A. Hamoud and K.P. Ghadle, Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind, Tamkang Journal of Mathematics, 49 (2018), no. 4, 301-315. https://doi.org/10.5556/j.tkjm.49.2018.2718
- A.A. Hamoud, M. Bani Issa, and K.P. Ghadle, M. Abdulghani, Existence and convergence results for caputo fractional Volterra integro-differential equations, Journal of Mathematics and Applications, 41 (2018), 109-122.
- A.A. Hamoud, N.M. Mohammed, K.P. Ghadle, and S.L. Dhondge, Solving integro-differential equations by using numerical techniques, International Journal of Applied Engineering Research, 14 (2019), no. 14, 3219-3225.
- A.A. Hamoud, M. Bani Issa, and K.P. Ghadle, Existence and uniqueness results for nonlinear Volterra-Fredholm integro-differential equations, Nonlinear Functional Analysis and Applications, 23 (2018), no. 4, 797-805. https://doi.org/10.22771/NFAA.2018.23.04.15
- A.M. Jerri, Introduction to Integral Equations with Applications, New York, Wiley, 1999.
- J. Manafianheris, Solving the integro-differential equations using the modified Laplace Adomian decomposition method, Journal of Mathematical Extension, 6 (2012), no. 1, 41-55.
- H.R. Marzban and S.M. Hoseini, Solution of nonlinear Volterra-Fredholm integro-differential equations via hybrid of Block-Pulse functions and Lagrange interpolating polynomials, Hindawi Publishing Corporation, Advances in Numerical Analysis, 868 (2012), no. 279, 1-14.
- S.B. Shadan, The use of iterative method to solve two-dimensional nonlinear Volterra-Fredholm integro-differential equations, J. of Communication in Numerical Analysis, (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, Linear and Nonlinear Integral Equations Methods and Applications, Springer Heidelberg Dordrecht London New York, 2011.
- A.M. Wazwaz, The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations, Appl. Math. Comput., 216 (2010), 1304-1309. https://doi.org/10.1016/j.amc.2010.02.023
- A.M. Wazwaz, A reliable modification of Adomian decomposition method, Appl. Math. Comput., 102 (1999), 77-86. https://doi.org/10.1016/S0096-3003(98)10024-3