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

I^2σ₀₊ y(t) +a·I^σ₀₊ y(t) +b·y(t)=tⁿ,

and

I^2σ₀₊ y(t) +a·I^σ₀₊ y(t) +b·y(t)=tⁿe^t,

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.