Keywords and phrases: trial solution, characteristic equation, telegraph equation.
Received: January 3, 2022; Accepted: February 22, 2022; Published: March 15, 2022
How to cite this article: Hwajoon Kim, Kamsing Nonlaopon and Supaknaree Sattaso, Basis of telegraph equations for lossless transmission lines obtained by Laplace transform, JP Journal of Heat and Mass Transfer 26 (2022), 81-89. http://dx.doi.org/10.17654/0973576322014
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] F. B. M. Belgacem and R. Silambarasan, Theory of natural transform, Mathematics in Engineering, Science and Aerospace 3 (2012), 105-135. [2] J. Bertrand, P. Bertrand and J. P. Ovarlez, The Mellin transform, the transforms and applications, Handbook, A. D. Poularkas, ed., CRC Press, Boca Raton, FL, 1996. [3] T. M. Elzaki and E. M. A. Hilal, Analytical solution for telegraph equation by modified of Sumudu transform “Elzaki Transform”, Mathematical Theory and Modeling 2 (2012), 104-111. [4] Y. H. Geum, A. K. Rathie and Hj. Kim, Matrix expression of convolution and its generalized continuous form, Symmetry 12(11) (2020), 1791. [5] Jy. Jang and Hj. Kim, An application of monotone convergence theorem in PDEs and Fourier analysis, Far East J. Math. Sci. (FJMS) 98(5) (2015), 665-669. [6] S. Jhanthanam, K. Nonlaopon and S. Orankitjaroen, Generalized solutions of the third-order Cauchy-Euler equation in the space of right-sided distributions via Laplace transform, Mathematics 7 (2019), 376. [7] Hj. Kim, The intrinsic structure and properties of Laplace-typed integral transforms, Math. Probl. Eng. 2017 (2017), 1-8. [8] Hj. Kim, The solution of the heat equation without boundary conditions, Dynam. Systems Appl. 27 (2018), 653-662. [9] Hj. Kim, Applications of an extended Laplace transform in heat equation, JP Journal of Heat and Mass Transfer 19(1) (2020), 185-193. [10] S. Jirakulchaiwong, K. Nonlaopon, J. Tariboon, S. K. Ntouyas and Hj. Kim, On -analogues of Laplace-typed integral transforms and applications, Symmetry 13 (2021), 631. https://www.mdpi.com/journal/symmetry [11] W. Koepf, I. S. Kim and Arjun K. Rathie, On a new class of Laplace-type integrals involving generalized hypergeometric functions, Axioms 8 (2019), 1-21. [12] E. Kreyszig, Advanced Engineering Mathematics, Wiley, Singapore, 2013. [13] Mohand M. A. Mahgoub, The new integral transform ‘Mohand Transform’, Advances in Theoretical and Applied Mathematics 12 (2017), 113-120. [14] T. Peter, The Radon transform, Theory and Implementation, Ph.D. Dissertation, Technical University of Denmark, Copenhagen, 1996. [15] Arjun K. Rathie, Y. H. Geum and Hj. Kim, A note on certain Laplace transforms of convolution-type integrals involving product of two generalized hypergeometric functions, Math. Probl. Eng. 2021, Art. ID 8827275, 15 pp. https://doi.org/10.1155/2021/8827275 [16] S. Supaknaree, K. Nonlaopon and Hj. Kim, Further properties of Laplace-type integral transforms, Dynam. Systems Appl. 28 (2019), 195-215. [17] T. Sung, I. Kim and Arjun K. Rathie, On a new class of Eulerian’s type integrals involving generalized hypergeometric functions, Aust. J. Math. Anal. Appl. 16 (2019), 1-15. [18] G. K. Watugula, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Integrated Education 24 (1993), 35-43.
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