The solutions of some certain non-homogeneous fractional integral equations
Abstract
In this paper, we propose the solutions of non-homogeneous fractional integral equations of the form
I2σ0+ y(t) +a·Iσ0+ y(t) +b·y(t)=tn,
and
I2σ0+ y(t) +a·Iσ0+ y(t) +b·y(t)=tnet,
where I σ 0+ is the Riemann-Liouville fractional integral of order σ = 1/2, σ=1, n∈N∪{0}, t∈R+, and a, b are constants, by using the Laplace transform technique. We obtain the solutions of these equations are in the form of Mellin-Ross function and in the form of exponential function.Copyright © 2021 Karuna Kaewnimit, Kamsing Nonlaopon, Somsak Orankitjaroen, Hwajoon Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
K. Kaewnimit, K. Nonlaopon, S. Orankitjaroen, H. Kim, The solutions of some certain non-homogeneous fractional integral equations, J. Math. Comput. Sci. 11 (2021), 6999–7014. https://doi.org/10.28919/jmcs/6179
BibTeX
@article{Kaewnimit2021,
author = {Kaewnimit, Karuna and Nonlaopon, Kamsing and Orankitjaroen, Somsak and Kim, Hwajoon},
title = {The solutions of some certain non-homogeneous fractional integral equations},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {6999--7014},
doi = {10.28919/jmcs/6179}
}