Solution of the Volterra integro-differential equations by the triple Elzaki transform ∗

Adil Mousa; Tarig M Elzaki

doi:10.48165/

Authors

Adil Mousa Department of Mathematics, Faculty of Science and Technology, Omdurman Islamic University, Khartoum, Sudan.
Tarig M Elzaki partment of Mathematics, Faculty of Sciences and Arts-Alkamil, University of Jeddah, Jeddah, Saudi Arabia.

DOI:

https://doi.org/10.48165/

Keywords:

Triple Elzaki transform, Inverse Triple Elzaki transform, partial integro differential equations, Upadhyaya transform, triple Upadhyaya transform

Abstract

In this paper we discuss the application of the various properties of the triple Elzaki transform to solve the linear Volterra integro-differential equations in three dimensions.

References

Wazwaz, Abdul Majid (2009). Partial Differential Equations and Solitary Waves Theory, Higher Education Press Beijing and Springer-Verlag, Berlin Heidelberg.

Moghadam, M.M., Saeedi, H. (2010). Application of differential transforms for solving the Volterra integro-partial differential equations, Iranian Journal of Science and Technology, Transaction A, 34(A1):59

Eltayeb, Hassan and Kilicman, Adem (2010). On double Sumudu transform and double Laplace transform, Malaysian Journal of Mathematical Sciences, 4(1), 17–30.

Elzaki, Tarig M. and Mousa, Adil (2019). On the convergence of triple Elzaki transform, SN Applied Sciences, 1:275. doi:10.1007/s42452-019-0257-2

Eltayeb, Hassan and Kilicman, Adem (2013). A note on double Laplace transform and Tele graphic equation, Abstract and Applied Analysis, Volume 2013, Article ID 932578, 6 pages http://dx.doi.org/10.1155/2013/932578.

Dhunde, Ranjit R. and Waghmare, G.L. (2015). Solving partial integro-differential equations using double Laplace transform method, American Journal of Computational and Applied Mathematics, 5(1), 7–10.

Bhadane, Prem Kiran G., Pradhan, V.H. and Desale, Satish V. (2013). Elzaki transform solution of one dimensional groundwater recharge through spreading, International Journal of Engineering Research and Applications, (ISSN 2248–9622), 3(6), 1607–1610.

Atangana, Abdon (2013). A note on the triple Laplace transform and its applications to some kind of third order differential equation, Abstract and Applied Analysis, Article ID 769102, 10 pages. [9] Elzaki, Tarig M. and Elzaki, Salih M. (2011). Application of new transform “Elzaki Transform” to partial differential equations, Global Journal of Pure and Applied Mathematics, (ISSN 0973-1768), 7(1), 65–70.

Elzaki, Tarig M. and Elzaki, Salih M. (2011). On connection between Laplace transform and Elzaki Transform, Advances in Theoretical and Applied Mathematics, (ISSN 0973-4554), 6(1), 1–11. [11] Elzaki, Tarig M., Elzaki, Salih M. and Elnour, Elsayed A. (2012). On the new integral transform

“Elzaki Transform” fundamental properties investigation and application, Global Journal of Pure and Applied Mathematics, (ISSN 0973-1768), 4(1), 1–13.

Elzaki, Tarig M. (2011). The new integral transform “Elzaki transform”, Global Journal of Pure and Applied Mathematics, 7(1), 57–64.

Elzaki, Tarig M. (2012). Solution of nonlinear differential equations using mixture of Elzaki trans form and differential transform method, International Mathematical Forum, 7(13), 631–638. [14] Mirzaee, Farshid and Hadadiyan, Elham (2016). Three-dimensional triangular functions and their

applications for solving nonlinear mixed VolterraFredholm integral equations, Alexandria Engi neering Journal, 55, 2943–2952.

Manafian, Jalil and Bolghar, Peyman (2018). Numerical solutions of nonlinear 3-dimensional Volterra integral-differential equations with 3D-block-pulse functions, Mathematical Methods in the Applied Sciences, (First published: 09 May 2018), 1–10. wileyonlinelibrary.com/journal/mma, doi: 10.1002/mma.4936.

Volterra integro-differential equations ... 569

Upadhyaya, Lalit Mohan (2019). Introducing the Upadhyaya integral transform, Bulletin of Pure and Applied Sciences, Section E, Mathematics and Statistics, 38E(1), 471–510. doi: 10.5958/2320- 3226.2019.00051.1

Watugala, G.K. (1993). Sumudu transform: a new integral transform to solve differential equations and control engineering problems, International Journal of Mathematical Education in Science and Technology, 24(1), 35–43.