The solutions of some certain non-homogeneous fractional integral equations

Karuna Kaewnimit, Kamsing Nonlaopon, Somsak Orankitjaroen, Hwajoon Kim

Abstract


In this paper, we propose the solutions of non-homogeneous fractional integral equations of the form

I0+ y(t) +a·Iσ0+ y(t) +b·y(t)=tn,

and

I0+ 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.

Full Text: PDF

Published: 2021-08-30

How to Cite this Article:

Karuna Kaewnimit, Kamsing Nonlaopon, Somsak Orankitjaroen, Hwajoon Kim, The solutions of some certain non-homogeneous fractional integral equations, J. Math. Comput. Sci., 11 (2021), 6999-7014

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.

 

Copyright ©2022 JMCS