Direct methods for singular integral equations and non-homogeneous parabolic PDEs




Laplace transform, L2-transform, modified Bessel function, Post-Widder transform
Abstract views: 205


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.


Download data is not yet available.


A.Aghili, Solution to time fractional non-homogeneous first order PDE with non-constant coefficients, Tbilisi Mathematical Journal 12(4) (2019), pp.149-155. DOI:

A.Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019), pp. 33-44. DOI:

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. DOI:

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. DOI:

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. DOI:

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. DOI:

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. DOI:




How to Cite

Aghili, A. (2022). Direct methods for singular integral equations and non-homogeneous parabolic PDEs. J. Numer. Anal. Approx. Theory, 51(2), 109–123.