On Double Laplace-Shehu Transform and its Properties with Applications

Year 2023, Volume: 15 Issue: 2, 218 - 226, 31.12.2023

Mona Hunaıber Alı Al-aatı

https://doi.org/10.47000/tjmcs.1009950

Abstract

In this paper, we introduce a new method for solving some partial differential equations called double Laplace-Shehu transform, some useful properties for the transform are presented. In addition, we use this transform to solve the Laplace, Poisson, Wave and Heat equations and find Laplace-Shehu transform for some functions.

Keywords

Double Laplace-Shehu transform, Laplace transform, Shehu transform, partial differential equations

References

• Aggarwal, S., Singh, A., Kumar, A., Kumar, N., Application of Laplace transform for solving improper integrals whose integrand consisting error function, Journal of Advanced Research in Applied Mathematics and Statistics, 4(2019), 1–7.
• Ahmed, S.A., Elzaki, T.M., Elbadri, M., Mohamed, M., Solution of partial differential equations by new double integral transform (Laplace -Sumudu transform), Ain Shams Engineering Journal, 12(2021), 4045–4049.
• Albukhuttar, A., Jubear, B., Neamah, M., Solve the Laplace, Poisson and telegraph equations using the Shehu transform, Turkish Journal of Computer and Mathematics Education, Turkey, 10(2021), 1759–1768.
• Albukhuttar, A., Ridha, Z., Kadhim, H., Applications of a Shehu transform to the heat and transport equations, International Journal of Psychosocial Rehabilitation, 24(2020), 4254–4263.
• Alfaqeih, S., Misirli, E., On double Shehu transform and its properties with applications, International Journal of Analysis and Applications, 3(2020), 381–395.
• Alkaleeli, S., Mtawal, A., Hmad, M., Triple Shehu transform and its properties with applications, African Journal of Mathematics and Computer, 14(2021), 4–12.
• Debnath, L., The double Laplace transforms and their properties with applications to functional, integral and partial differential equations, Int. J. Appl. Comput. Math, 2(2016), 223–241.
• Dhunde, R.,Waghmare, G., Double Laplace transform method in mathematical physics, International Journal of Theoretical and Mathematical Physics, 7(2017), 14–20.
• Eltayeb, H., Kilicman, A., A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform, Applied Mathematics Letters 21(2008), 1324–1329.
• Lakmon, K., Mensah, Y., The Plancherel formula for the Shehu transform, Annals of Pure and Applied Mathematical Sciences, 1(2021) 14–19.
• Maitama, S., Zhao, W., New integral transfrom: Shehu transform a generalizattion of Sumudu and Laplace transfrom for solving differential equations, International Journal of Analysis and Applications, 17(2019), 167–190.