Solving delay differential equations via Sumudu transform

[1] A.T. Ademola, S. Moyo, B.S. Ogundare, M.O. Ogundiran and O.A. Adesina, New conditions on the solutions of a certain third order delay differential equations with multiple deviating arguments, Diff. Equ. Control Process. 2019 (2019), no. 1, 33–69.

[2] W.G. Ajello, H.I. Freedman and J. Wu, A model of stage structured population growth with density depended time delay, SIAM J. Appl. Math. 52 (1992), 855–869.

[3] W.R.A. AL-Hussein and S.N. Al-Azzawi, Approximate solutions for fractional delay differential equations by using Sumudu transform method AIP Conf. Proc. 2096 (2019), no. 1, 020007.

[4] A.K. Alomari, M.I. Syam, N. R. Anakira and A.F. Jameel, Homotopy Sumudu transform method for solving applications in physics, Results Phys.18 (2020), 103265.

[5] A. Arikoglu and I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform method, Chaos Solitons Fractals, 34, (2007), 1473-1481.

[6] M.M. Bashi and M. Cevik, Numerical solution of pantograph-type delay differential equations using perturbation iteration algorithms, J. Appl. Math. 2015 (2015), Article ID: 139821, 10 pages.

[7] M.D. Buhmann and A. Iserles, Stability of the discretized pantograph differential equation, Math. Comp. 60 (1993), 575–589.

[8] A.K. Golmankhaneh and C. Tunς, Sumudu transform in fractal calculus, Appl. Math. Comput. 350 (2019), no. 1, 386–401.

[9] J.R. Graef and C. Tunς, Global asymptotic stability and boundedness of certain multi-delay functional differential equations of third order, Math. Methods Appl. Sci. 38 (2015), no. 17, 3747–3752.

[10] J. He, Variational iteration method a kind of non-linear analytical technique: Some examples, Int. J. Non-Linear Mech. 34 (1999), no. 4, 699–708.

[11] J. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. 207 (2007), no. 1, 3–17.

[12] J.H. He and X.H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. 54 (2007), no. 7-8, 881–894.

[13] J.H. He, G.C. Wu andF. Austin, The variational iteration method which should be followed, Nonlinear Sci. Lett. A 1 (2010), no. 1, 1–30.

[14] N. Herisanu, V. Marinca, A modifed variational iteration method for strongly nonlinear problems, Nonlinear Sci. Lett. A: Math. Phys. Mech. 1 (2010), no. 2, 183–192.

[15] X.H. Ma and C.M. Huang, Numerical solution of fractional integro-differential equations by a hybrid collocation method, Appl. Math. Comput. 219 (2013), 6750–6760.

[16] Z. Meng, L. Wang, H. Li and W. Zhang, Legendre wavelets method for solving fractional integro-differential equations, Int. J. Comput. Math. 92 (2015), 1275–1291.

[17] S.V. Meleshko, S. Moyo and G.F. Oguis, On the group classification of systems of two linear second-order ordinary differential equations with constant coefficients, J. Math. Anal. Appl. 410 (2014), no. 1, 341–347.

[18] T.G. Mkhize, K. Govinder, S. Moyo and S.V. Meleshko, Linearization criteria for systems of two second-order stochastic ordinary differential equations, Appl. Math. Comput. 301 (2017), 25–35.

[19] S.A. Mohammed and C. Tunς, Qualitative analysis of nonlinear retarded differential equations of second order, Dynamic Syst. Appl. 29 (2020), 53–70. equations with constant coefficients, J. Math. Anal. Appl. 410 (2014), 341–347.

[20] S. Momani and M.A. Noor, Numerical methods for fourth-order fractional integro-differential equations, Appl. Math. Comput. 182 (2006), 754–760.

[21] K.S. Nisar, A. Shaikh, G. Rahman and D. Kumar, Solution of fractional kinetic equations involving class of functions and Sumudu transform, Adv. Differ. Equ. 2020 (2020), Article Number 39.

[22] A.H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, NY, USA, 1981.

[23] Y. Nawaz, Variational iteration method and homotopy perturbation method for fourth-order fractional integrodifferential equations, Comput. Math. Appl. 61 (2011), 2330–2341.

[24] J.R. Ockendon and A.B. Tayler, The dynamics of a current collection system for an electric locomotive, Proc. R. Soc. Lond. Ser. A. 322 (1971), no. 1551, 447–468.

[25] Z.A. Odibat, A study on the convergence of variational iteration method, Math. Comput. Model. 51 (2010), 1181–1192.

[26] E. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006), 1–6.

[27] A. Saadatmandi and M. Dehghan, Variational iteration method for solving a generalized pantograph equation, Comput. Math. Appl. 58 (2009), no. 11-12, 2190–2196.

[28] H. Saeedi and M. Mohseni Moghadam, Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1216–1226.

[29] H. Saeedi, M. Mohseni Moghadam, N. Mollahasani and G.N. Chuev, A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1154–1163.

[30] K. Sayevand, Analytical treatment of Volterra integro-differential equations of fractional order, Appl. Math. Model. 39 (2015), 4330–4336.

[31] M. Sezer and A. Akyuz-Dascioglu, A Taylor method for numerical solution of generalized pantograph equations with linear functional argument, J. Comput. Appl. Math. 200 (2007), 217–225.

[32] M. Sezer, S. Yalcinbas and N. Sahin, Approximate solution of multi-pantograph equation with variable coefficients, J. Comput. Appl. Math. 214 (2008), 406–416.

[33] S. Vilu, R.R. Ahmad and U.K. Salma Din, Variational iteration method and Sumudu transform for solving delay differential equation, Int. J. Differ. Equ. 2019 (2019), Article ID 6306120, 6 pages.

[34] Y.X. Wang and L. Zhu, SCW method for solving the fractional integro-differential equations with a weakly singular kernel, Appl. Math. Comput. 275 (2016), 72–80.

[35] G.K. Watugala, Sumudu transform a new integral transform to solve differential equations and control engineering problems, Math. Engin. Ind. 24 (1993), no. 1, 35–43.

[36] J. Wei and T. Tian, Numerical solution of nonlinear Volterra integro-differential equations of fractional order by the reproducing kernel method, Appl. Math. Model. 39 (2015), 4871–4876.

[37] G. Wu, Challenge in the variational iteration method a new approach to the identification of the Lagrange multipliers, J. King Saud Univ. Sci. 25 (2013), no. 2, 175–178.
[38] G. Wu and D. Baleanu, Variational iteration method for fractional calculus a universal approach by Laplace transform, Adv. Differ. Equ. 2013 (2013), no. 1, 1–9.

[39] Z.-H. Yu, Variational iteration method for solving the multi-pantograph delay equation, Phys. Lett. A 372 (2008), no. 43, 6475–6479.

[40] L. Zhu and Q.B. Fan, Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 2333–2341.

[41] L. Zhu and Q.B. Fan, Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), 1203–1213.