Direct methods for singular integral equations and non-homogeneous parabolic PDEs
Keywords:Laplace transform, L2-transform, modified Bessel function, Post-Widder transform
In this article, the author presented some applications of the Laplace, \(L^2\), and Post-Widder transforms for solving fractional Singular Integral Equations, impulsive differential equation and systems of differential equations. Finally, analytic solution for a non-homogeneous partial differential equation with non-constant coefficients is given. The obtained results reveal that the integral transform method is an effective tool and convenient.
A.Aghili, Solution to time fractional non-homogeneous first order PDE with non-constant coefficients, Tbilisi Mathematical Journal 12(4) (2019), pp.149-155. https://doi.org/10.32513/tbilisi/1578020577 DOI: https://doi.org/10.32513/tbilisi/1578020577
A.Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019), pp. 33-44. https://doi.org/10.32513/tbilisi/1553565624 DOI: https://doi.org/10.32513/tbilisi/1553565624
A.Aghili, A. Ansari, Solving partial fractional differential equations using the LA-transform, Asian-European Journal of Mathematics, vol. 3 no.2 (2010) pp.209-220. https://doi.org/10.1142/S1793557110000143 DOI: https://doi.org/10.1142/S1793557110000143
A.Aghili, Complete solution for the time fractional diffusion problem with mixed boundary conditions by operational method, Applied Mathematics and Nonlinear Sciences, vol. 6 (2020) no. 1, pp. 9-20. https://doi.org/10.2478/amns.2020.2.00002 DOI: https://doi.org/10.2478/amns.2020.2.00002
A. Aghili, Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms, J. Numer. Anal. Approx. Theory, vol. 50 (2021) no. 1, pp.12-26. https://doi.org/10.33993/jnaat501-1240 DOI: https://doi.org/10.33993/jnaat501-1240
A.Apelblat, Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
H.J. Glaeske, A.P.Prudnikov, K. A. Skornik, Operational calculus and related topics.Chapman and Hall / CRC 2006. https://doi.org/10.1201/9781420011494 DOI: https://doi.org/10.1201/9781420011494
I.Podlubny, Fractional differential equations, Academic Press, New York (1999).
S.Prossdorf, B. Silberman, Numerical analysis for integral and related operator equations, Academie Verlag, Berlin, (1991)
O.Yurekli, I.Sadek,A Parseval-Goldstein type theorem on the Widder potential transform and its applications, International Journal of Mathematics and Mathematical Sciences, 14(1991), pp.517-524. https://doi.org/10.1155/S0161171291000704 DOI: https://doi.org/10.1155/S0161171291000704
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Copyright (c) 2022 Arman Aghili
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