Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms
DOI:
https://doi.org/10.33993/jnaat501-1240Keywords:
Laplace transform, Fourier transform, Hankel transform, Riemann-Liouville fractional derivative, Caputo fractional derivative, Modified Bessel functions, Stieltjes transform, Heat conduction, Fokker-Planck equationAbstract
In this article, the author implemented the joint transform method, for solving the boundary value problems of time fractional heat equation. The results reveal that the integral transform method is reliable and efficient. Illustrative examples are also provided.
Downloads
References
A. Aghili, Solution to time fractional non-homogeneous first order PDE with non-constant coefficients. Tbilisi Mathematical Journal 12 (2019) 4, pp. 149–155, https://doi.org/10.32513/tbilisi/1578020577
A. Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (2019) 1, pp. 33-44, http://doi.org/10.32513/tbilisi/1553565624
A. Aghili, Fractional Black-Scholes equation. International Journal of Financial Engineering, Vol. 4, No. 1 (2017) 1750004 (15 pages), https://doi.org/10.1142/S2424786317500049
A. Aghili, Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method, Applied Mathematics and Nonlinear Sciences, 2020 (AOP) pp. 9-20, https://doi.org/10.2478/amns.2020.2.00002
A. Apelblat, Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
G. Dattoli, P.L. Ottaviani, A. Torr, I. Vazquez, Evolution operator equations: integration with algebraic and finite difference methods.Applications to physical problemsin classical and quantum mechanics and quantum field theory. Riv.Nuovo. Cimento Soc. Ital. Fis.(Ser. 4) 20 (1997) 2, pp. 1-133, https://doi.org/10.1007/bf02907529
G. Dattoli, H.M. Srivastava, K.V. Zhukovsky. Operational methods and differential equations to initial – value problems. Applied Mathematics and computations.184 (2007) pp. 979-1001, https://doi.org/10.1016/j.amc.2006.07.001
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, North Holand Mathematics Studies, 204, Elsevier Science Publishers, Amesterdam, Heidelberg and New York, 2006.
F. Mainardi, G. Paganini, R.K. Saxena, Fox H functions in fractional diffusion. Journal of Computational and Applied Mathematics 178 (2005), pp. 321-331, https://doi.org/10.1016/j.cam.2004.08.006
I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA, 1999.
Y.Z. Povstenko, Fractional radial diffusion in a cylinder, Journal of Molecular Liquides 137 (2008), pp. 46-50, https://doi.org.doi.org/10.1016/j.molliq.2007.03.006
W. Schneider, W. Wyss, Fractional diffusion and wave equations, J. Math. Phys. 27 (1989), pp. 134-144, https://doi.org.https//doi.org/10.1063/1.528578
S.P. Zhou, G.KL. He, T.F. Xie,On a class of fractals: the constructive structure. Chaos, Solitons and Fractals 2004; (19) 1099-1104, https://doi.org/10.1016/s0960-0779(03)00282-0
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
