37
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Numerical solution of fractional-order integro-differential equations using Laguerre wavelet method

&
Pages 643-662 | Received 01 Nov 2020, Published online: 13 Jun 2022

References

  • Alshammari, S., Al-Smadi, M., Hashim, I., Alias, M.A. (2019), “Applications of Fractional Power Series Approach in Solving Fractional Volterra Integro-Differential Equations”, AIP Conf. Proc. 2111, pp.020003-1–020003-7; https://doi.org/10.1063/1.5111210
  • Doha, E.H., Abdelkawy, M.A., Amin, A.Z.M., Baleanu, D. (2017), “Spectral technique for solving variable-order fractional Volterra integro-differential equations”, Numer Methods Partial Differential Eq., pp.1–19.
  • Elbeleze, A.A., Kılıcman, A., Taib, B.M. (2016), “Approximate solution of integro-differential equation of fractional (arbitrary) order”, Journal of King Saud University - Science, Vol.28 No.1, pp.61-68. doi: 10.1016/j.jksus.2015.04.006
  • Hamoud, A.A., Ghadle, K.P., Pathade, P.A. (2019), “An existence and convergence results for caputo fractional volterra integro-differential equations”, Jordan Journal of Mathematics and Statistics (JJMS), Vol.12 No.3, pp.307–327.
  • Jiang, W., Tian, T. (2015) “Numerical solution of nonlinear Volterra integro-differential equations of fractional order by the reproducing kernel method”, Appl. Math. Modelling, vol. 39, pp.4871-4876, doi: http://doi.org/10.1016/j.apm.2015.03.053
  • Kumbinarasaiah, S. (2020), “A new approach for the numerical solution for nonlinear Klein–Gordon equation”, SeMA, Vol. 77, pp.435-456. doi: 10.1007/s40324-020-00225-y
  • Kumbinarasaiah, S., Rezazadeh, H. (2020) “Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique”, International Journal of Nonlinear Sciences and Numerical Simulation, https://doi.org/10.1515/ijnsns-2019-0300.
  • Kumbinarasaiah, S., Mundewadi, R.A. (2019), “Numerical Method for the Solution of Abel's Integral Equations using Laguerre Wavelet”, Journal of Information and Computing Science, Vol. 14 No. 4, pp.250-258
  • Mundewadi, R.A., Kumbinarasaiah, S. (2019), “Numerical Solution of Abel's Integral Equations using Hermite Wavelet”, Applied Mathematics and Nonlinear Sciences, Vol. 4 No. 1, pp.181-192 doi: 10.2478/AMNS.2019.1.00017
  • Mundewadi, R.A., Mundewadi, B.A. (2018), “Hermite Wavelet Collocation Method for the Numerical Solution of Integral and Integro-Differential Equations”, International Journal of Mathematics Trends and Technology (IJMTT), Vol. 53 No. 3, pp.215-231 doi: 10.14445/22315373/IJMTT-V53P527
  • Mundewadi, R.A., Mundewadi, B.A. (2018), “Haar Wavelet Collocation Method for the Numerical Solution of Integral and Integro-Differential Equations”, International Journal of Mathematics and its Applications, Vol. 6 No. 1, pp.1133-1149
  • Mundewadi, R.A., Mundewadi, B.A. (2018), “Legendre Wavelet Collocation Method for the Numerical Solution of Integral and Integro-Differential Equations”, International Journal of Advance in Management, Technology and Engineering Sciences, Vol. 8 No. 1, pp.151–170
  • Mundewadi, R.A., Mundewadi, B.A. (2020), “Numerical Solution of Linear and Nonlinear Integral and Integro-Differential Equations using Biorthogonal Spline Wavelet Transform Method”, Int. J. Math. And Appl., Vol. 8 No. 1, pp.7-32.
  • Mundewadi, R.A., Mundewadi, B.A., Kantli, M.H. (2020), “Iterative Scheme of Integral and Integro-differential Equations Using Daubechies Wavelets New Transform Method”, Int. J. Appl. Comput. Math., Vol. 6 No. 135, pp.1-30, https://doi.org/10.1007/s40819-020-00879-2
  • Saadatmandi, Dehghan, M. (2010), “A new operational matrix for solving fractional-order differential equations”, Computers and Mathematics with Applications, Vol. 59, pp.1326-1336. doi: 10.1016/j.camwa.2009.07.006
  • Saeedi, H., Mohseni Moghadam, M.M. (2011), “Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets”, Commun Nonlinear Sci Numer Simulat, Vol. 16, pp.1216–1226. doi: 10.1016/j.cnsns.2010.07.017
  • Shiralashetti, S.C., Mundewadi, R.A. (2016), “Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method”, Bulletin of Mathematical Sciences and Applications, Vol. 18, pp.50-59. doi: 10.18052/www.scipress.com/BMSA.18.50
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2019), “CAS wavelets analytic solution and Genocchi polynomials numerical solutions for the integral and Integro-differential equations”, J. Interdiscip. Math., Vol. 22 No. 3, pp.201–218 doi: 10.1080/09720502.2019.1602354
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2018), “Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems”, Alex. Eng. J., Vol. 57, pp.2591–2600
  • Shiralashetti, S.C., Kumbinarasaiah, S., Hoogar, B.S. (2017), “Hermite wavelet-based numerical method for the solution of linear and nonlinear delay differential equations”, Int. J. Eng. Sci. Math., Vol. 6 No. 8, pp.71–79
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2019), “New generalized operational matrix of integration to solve non-linear singular boundary value problems using Hermite wavelets”, Arab J. Basic Appl. Sci., Vol. 26 No. 1, pp.385–396 doi: 10.1080/25765299.2019.1646090
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2019), “Hermite wavelets method for the numerical solution of linear and nonlinear singular initial and boundary value problems”, Comput. Methods Differ. Equ., Vol. 7 No. 2, pp.177–198
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2017), “Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear lane-Emden type equations”, Appl. Math. Comput., Vol. 315, pp.591–602
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2018) “Cardinal B-spline wavelet-based numerical method for the solution of generalized Burgers–Huxley equation”, Int. J. Appl. Comput. Math., Vol. 4 No. 73, pp.1-13, https://doi.org/10.1007/s40819-018-0505-y
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2017), “Some results on haar wavelets matrix through linear algebra”, Wavelets Linear Algebra, Vol. 4 No. 2, pp.49–59.
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2019), “Some results on shannon wavelets and wavelets frames”, Int. J. Appl. Comput. Math., Vol. 5 No. 10, pp.1-15, https://doi.org/10.1007/s40819-018-0596-5
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2019), “Laguerre wavelets collocation method for the numerical solution of the Benjamina– Bona–Mohany equations”, Journal of Taibah University for Science, Vol. 13 No. 1, pp.9-15. doi: 10.1080/16583655.2018.1515324
  • Shiralashetti, S.C., Kumbinarasaiah, S. (2020), “Laguerre Wavelets Exact Parseval Frame-based Numerical Method for the Solution of System of Differential Equations”, Int. J. Appl. Comput. Math., Vol. 6 No. 101, pp.1-16, https://doi.org/10.1007/s40819-020-00848-9
  • Tohidi, E., Ezadkhah, M.M., Shateyi, S. (2014), “Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials”, Hindawi Publishing Corporation Abstract and Applied Analysis,Vol. 2014 No. 162896, pp.1-7, http://doi.org/10.1155/2014/162896
  • Tabharit, L., Dahmani, Z., (2020) “Integro-differential equations of arbitrary orders involving convergentseries”, Journal of Interdisciplinary Mathematics, vol. 23 No. 5, pp. 935-953, https://doi.org/10.1080/09720502.2020.1711603
  • Wang, Y., Zhu, L. (2017), “Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method”, Advances in Difference Equations, vol. 2017 No. 27, pp.1-16, https://doi.org/10.1186/s13662-017-1085-6
  • Zhu, L., Fan, Q. (2013), “Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW”, Commun Nonlinear Sci Numer Simulat, Vol. 18, pp.1203–1213. doi: 10.1016/j.cnsns.2012.09.024

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.