Laplace Transform Analytical Restructure

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References

[1] L. Debnath and D. Bhatta, “Integral Transforms and Their Applications,” 2nd Edition, C. R. C. Press, London, 2007.

[2] P. P. G. Dyke, “An Introduction to Laplace Transform and Fourier Series,” Springer-Verlag, London, 2004.

[3] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, “Tables of Integral transform,” Vol. 1, McGrawHill, New York, Toronto, London, 1954.

[4] M. Rahman, “Integral Equations and Their Applications,” WIT Press, Boston, 2007.

[5] J. L. Schiff, “Laplace Transform Theory and Applications,” Springer, Auckland, 2005.

[6] M. R. Spiegel, “Theory and Problems of Laplace Transforms,” Schaums Outline Series, McGraw-Hill, New York, 1965.

[7] W. T. Thomson, “Laplace Transformation Theory and Engineering Applications,” Prentice-Hall Engg Design Series, Printice-Hall Inc., New York, 1950.

[8] D. V. Widder, “The Laplace Transform,” Oxford University Press, London, 1946.

[9] F. B. M. Belgacem, A. A. Karaballi and S. L. Kalla, “Analytical Investigations of the Sumudu Transform and Applications to Integral Production Equations,” Mathematical Problems in Engineering (MPE), Vol. 2003, No. 3, 2003, pp. 103-118.

[10] F. B. M. Belgacem and A. A. Karaballi, “Sumudu Transform Fundamental Properties Investigations and Applications,” Journal of Applied Mathematics and Stochastic Analysis (JAMSA), 2005, Article ID: 91083.

[11] F. B. M. Belgacem, “Introducing and Analysing Deeper Sumudu Properties,” Nonlinear Studies Journal (NSJ), Vol. 13, No. 1, 2006, pp. 23-41.

[12] F. B. M. Belgacem, “Applications of Sumudu Transform to Indefinite Periodic Parabolic Equations,” In: Proceedings of the 6th International Conference on Mathematical Problems & Aerospace Sciences (ICNPAA 06), Chap. 6, Cambridge Scientific Publishers, Cambridge, 2007, pp 51-60.

[13] F. B. M. Belgacem, “Sumudu Applications to Maxwell’s Equations,” PIERS Online, Vol. 5, No. 4, 2009, pp 355360. doi:10.2529/PIERS090120050621

[14] F. B. M. Belgacem, “Sumudu Transform Applications to Bessel’s Functions and Equations,” Applied Mathematical Sciences, Vol. 4, No. 74, 2010, pp. 3665-3686.

[15] M. G. M. Hussain and F. B. M. Belgacem, “Transient Solutions of Maxwell’s Equations Based on Sumudu Transform,” Journal of Progress in Electromagnetics Research (PIER), Vol. 74, 2007, pp. 273-289.
doi:10.2528/PIER07050904

[16] M. A. Rana, A. M. Siddiqui, Q. K. Ghori and R. Qamar, “Application of He’s Homotopy Perturbation Method to Sumudu Transform,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. 2, 2007, pp. 185-190.

[17] F. B. M. Belgacem and R. Silambarasan, “Theory of the Natural Transform,” Mathematics in Engineering, Science and Aerospace (MESA) Journal, Vol. 3, No. 1, 2012, pp. 99-124.

[18] F. B. M. Belgacem and R. Silambarasan, “Maxwell’s Equations Solutions by Means of the Natural Transform,” Mathematics in Engineering, Science and Aerospace (MESA) Journal, Vol. 3, No. 3, 2012, pp. 313-323.

[19] F. B. M. Belgacem and R. Silambarasan, “The Generalized n-th Order Maxwell’s Equations,” PIERS Proceedings, Moscow, 19-23 August 2012, pp. 500-503.

[20] F. B. M. Belgacem and R. Silambarasan, “Advances in the Natural Transform,” AIP Conference Proceedings, Vol. 1493, 2012, pp. 106-110. doi:10.1063/1.4765477

[21] R. Silambarasan and F. B. M. Belgacem, “Applications of the Natural Transform to Maxwell’s Equations,” PIERS Proceedings, Suzhou, 12-16 September 2011, pp. 899902.

[22] S. Abbasbandy, “Application of He’s Homotopy Perturbation Method for Laplace Transform,” Journal of Chaos, Solitons and Fractals, Vol. 30, No. 5, 2006, pp. 12061212. doi:10.1016/j.chaos.2005.08.178

[23] E. Babolian, J. Biazar and A. R. Vahidi, “A New Computational Method for Laplace Transform by Decomposition Method,” Journal of Applied Mathematics and Computation, Vol. 150, No. 3, 2004, pp. 841-846.
doi:10.1016/S0096-3003(03)00312-6

[24] C. J. Efthimiou, “Trigonometric Series via Laplace Transform,” 2007. http://arxiv.org/abs/0707.3590v1

[25] S. Saitoh, “Theory of Reproducing Kernels: Applications to Approximate Solutions of Bounded Linear Operator Equations on Hilbert Spaces,” American Mathematical Society Translations, Vol. 230, No. 2, 2010, pp. 107-134.