Laplace Inverse Transform for Functions of Type nth Root of a Product of Linear Factors

DOI: 10.4236/oalib.1103741, PP. 1-11

Keywords: Laplace Inverse Transform, Multivalued Functions, Integration Contour, Stehfest Numerical Method

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Abstract:

In this work, we present four results for the Laplace inverse transform of functions that involve the nth root of a product of linear factors. In order to find the Laplace inverse transform, we considered a branch cut for the nth root and a region of suitable integration, to avoid the branching points. Due to that, the solution is in terms of integrals, we easily approach this solution for some specific parameters.

References

[1]	Arciga, M.P., Ariza, F.J., Sanchez, J. and Salmeron, U. (2016) Fractional Stochastic Heat Equation on the Half-Line. Applied Mathematical Sciences, 10, 3095-3105. https://doi.org/10.12988/ams.2016.69243
[2]	Di Paola, M., Pirrotta, A. and Valenza, A. (2011) Visco-Elastic Behavior through Fractional Calculus: An Easier Method for Best Fitting Experimental Results. Mechanics of Materials, 43, 79-806. https://doi.org/10.1016/j.mechmat.2011.08.016
[3]	Ekoue, F., Halloy A.F., Gigon, D., Plantamp, G. and Zajdman, E. (2013) Maxwell-Cattaneo Regularization of Heat Equation. International Scholarly and Scientific Research and Innovation, 7, 772-775.
[4]	Golghanddashti, H. (2011) A New Analytically Derived Shape Factor for Gas-Oil Gravity Drainage Mechanism. Journal of Petroleum Science and Engineering, 77, 18-26. https://doi.org/10.1016/j.petrol.2011.02.004
[5]	Huan, X., Hai,Q. and Xiao, J. (2013) Fractional Cattaneo Heat Equation in a Semi Infinite Medium. Chinese Physics B, 22, 014401-1-014401-6. https://doi.org/10.1088/1674-1056/22/1/014401
[6]	Shu, L. and Bing, C. (2016) Generalized Variational Principles for Heat Conduction Models Based on Laplace Transforms. International Journal of Heat and Mass Transfer, 103, 1176-1180. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.065
[7]	Rehbinder, G. (1989) Darcyan Flow with Relaxation Effect. Applied Scientific Research, 46, 45-72. https://doi.org/10.1007/BF00420002
[8]	Hernndez, D., Nez, M. and Velasco, J. (2013) Telegraphic Double Porosity Models for Head Transient Behavior in Naturally Fractured Aquifers. Water Resources Research, 49, 4399-4408. https://doi.org/10.1002/wrcr.20347
[9]	Wu, Y., Ehlig-Economides, C., Qin, G., Kang, Z., Zhang, W., Ajayi, B. and Tao, Q. (2007) A Triple-Continuum Pressure-Transient Model for a Naturally Fractured Vuggy Reservoir. Lawrence Berkeley National Laboratory, Berkeley, CA. https://doi.org/10.2118/110044-MS
[10]	Stehfest, H. (1970) Algorithm 368: Numerical Inversion of Laplace Transforms [d5]. Communications of the ACM, 13, 47-49. https://doi.org/10.1145/361953.361969
[11]	Lfqvist, T. and Rehbinder, G. (1993) Transient Flow towards a Well in an Aquifer including the Effect of Fluid Inertia. Applied Scientific Research, 51, 611-623. https://doi.org/10.1007/BF00868003
[12]	Gradshteyn, I.S. and Ryzhik, I.M. (2014) Table of Integrals, Series, and Products. Academic Press, New York.
[13]	Abramowitz, M. and Stegun, I.A. (1964) Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Courier Corporation, New York.
[14]	Carslaw, H.S. and Jaeger, J.C. (1941) Operational Methods in Applied Mathematics, Dover, New York.

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