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Numerical Inversion Technique for the One and Two-Dimensional L2-Transform Using the Fourier Series and Its Application to Fractional Partial Differential Equations
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  • Journal title : Kyungpook mathematical journal
  • Volume 52, Issue 4,  2012, pp.383-395
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2012.52.4.383
 Title & Authors
Numerical Inversion Technique for the One and Two-Dimensional L2-Transform Using the Fourier Series and Its Application to Fractional Partial Differential Equations
Aghili, Arman; Ansari, Alireza;
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 Abstract
In this paper, we use a computational algorithm for the inversion of the one and two-dimensional -transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the -transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.
 Keywords
Laplace transform;-transform;Fourier series;Numerical inversion method;
 Language
English
 Cited by
 References
1.
A. Aghili, A. Ansari and A. Sedghi, An inversion technique for the L2-transform with applications, Inter. J. Contemp. Math. Sci., 2(28)(2007), 1387-1394.

2.
A. Aghili, A. Ansari, Complex inversion formula for stieltjes and widder transforms with applications, Inter. J. Contemp. Math. Sci., 3(16)(2008), 761-770.

3.
A. Aghili, A. Ansari, Solving partial fractional differential equations using the LA- transform, Asia-Euro. J. Math., 3(2)(2010), 209-220. crossref(new window)

4.
A. Aghili, F. Safarian, An Inversion technique for ${\varepsilon}_{2,1}$-transform with applications, Inter. J. Contemp. Math. Sci., 3(16)(2008), 771-780.

5.
K. Crump, Numerical inversion of Laplace transforms using a Fourier series approximation, Appl. Numer. Math., 23(1)(1976), 89-96.

6.
M. Dehghan, J. Manafian and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Numer. Meth. Part. Diff. Equ., 26(2010), 448-479.

7.
M. Dehghan, J. Manafian and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch, 65a(2010), 935-549.

8.
H. Dubner, J. Abate, Numerical inversion of Laplace transform by relating them to the finite Fourier cosine transform, Appl. Math. Comput., 15(1)(1968), 115-123.

9.
M. Lakestani, M. Dehghan and S. Irandoust-Pakchin, The construction of operational matrix of fractional derivatives using B-spline functions, Commun. Nonlinear Sci. Numer. Simul., 17(3)(2012), 1149-1162. crossref(new window)

10.
J. R. Macdonald, Accelerated convergence,divergence, iteration, extrapolation and curve-fitting, J. Appl. Phys., 17(1964), 3034-3041.

11.
M. V. Moorthy, Numerical inversion of two dimensional Laplace tranforms-fourier series representation, Appl. Numer. Math., 17(1995), 119-127. crossref(new window)

12.
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.

13.
A. Saadatmandi, M. Dehghan, A new operational matrix for solving fractionalorder differential equations, Comput. Math. Appl., 59(2010), 1326-1336. crossref(new window)

14.
A. Saadatmandi, M. Dehghan, A tau approach for solution of the space fractional diffusion equation, Comput Math Appl., 62(2011), 1135-1142. crossref(new window)

15.
P. N. Shankar, On the evolution of disturbances at an inviscid interface, J. Fluid. Mech., 108(1981), 159-170. crossref(new window)

16.
O. Yurekli, I. Sadek, A Parseval-Goldstein type theorem on the Widder potential transform and its applications, Inter. J. Math. Math. Sci., 14(1991), 517-524. crossref(new window)

17.
O. Yurekli, New identities involving the Laplace and the L2-transforms and their applications, Appl. Math. Comput., 99(1999), 141-151. crossref(new window)