The Solutions of Some Riemann–Liouville Fractional Integral Equations - Karuna Kaewnimit; Fongchan Wannalookkhee; Kamsing Nonlaopon; Somsak Orankitjaroen (Fractal and Fractional, 2021)
In this paper, we propose the solutions of nonhomogeneous fractional integral equations of the form <semantics><msubsup>I0+3σ</msubsup>y(t)+a·<msubsup>I0+2σ</msubsup>y(t)+b·<msubsup>I0+σ</msubsup>y(t)+c·y(t)=f(t),</semantics> where <semantics><msubsup>I0+σ</msubsup></semantics> is the Riemann–Liouville fractional integral of order <semantics>σ=1/3,1,f(t)=tn,tnet,n∈N∪{0},t∈R+,</semantics> and <semantics>a,b,c</semantics> are constants, by using the Laplace transform technique. We obtain solutions in the form of Mellin–Ross function and of exponential function. To illustrate our findings, some examples are exhibited.