Fourier, Laguerre, Laplace Transforms with Applications

In this article, the author considered certain time fractional equations using joint integral transforms. Transform method is a powerful tool for solving singular integral equations, integral equation with retarded argument, evaluation of certain integrals and solution of partial fractional differential equations. The obtained results reveal that the transform method is very convenient and effective. Illustrative examples are also provided.

Full text (pdf)

1. A. Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019) 33-44.
2. A. Aghili, Space-fractional transport equation, Konuralp Journal of Mathematics, 8 (2) (2020) 304-312.
3. A. Aghili, Some identities for Mellin, Kontorvich-Lebedev transforms with applications, Tbilisi Mathematical Journal 14 (2) (2021).
4. A. Aghili, H. Zeinali, Advances in Laplace type integral transforms with applications, Indian Journal of Science and Technology 7 (6) (2014) 877-890.
5. A. Aghili. New results involving Airy polynomials, fractional calculus and solution to generalized heat equation. New trends in mathematical sciences, Vol. 3, 2015.
6. A. Aghili, B. Salkhordeh Mogaddam, Laplace transform pairs of N-dimensions and second order linear partial differential equations with constant coefficients, Annales Mathematicae et Informaticae 35 (2008) 3-10, http://www.ektf.hu/ami
7. A. Apelblat, Laplace Transforms and Their Applications, Nova science publishers Inc., New York, 2012.
8. S. Das, A note on fractional diffusion equations, Chaos, Solitons and Fractals 42 (2009) 2074-2079.
9. B. Davies, Integral Transforms and Their Applications, Springer, USA, 2001.
10. F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett. (1996) 9:23-8.
11. F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solutions the space-time fractional diffusion-wave equation, Fract. Calculus Appl. Anal. 2001:4:153-92.
12. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
13. R.S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, World Scientific Publishing Co. Pte. Ltd., 2003.