Abstract
In this paper, we propose the solutions of nonhomogeneous fractional integral equations of the form I0+3σy(t)+a·I0+2σy(t)+b·I0+σy(t)+c·y(t)=f(t), where I0+σ is the Riemann–Liouville fractional integral of order σ=1/3,1,f(t)=tn,tnet,n∈N∪{0},t∈R+, and a,b,c 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.
Highlights
In this paper, we propose the solutions of nonhomogeneous fractional integral equations
Fractional calculus is the theory of derivatives and integrals of arbitrary complex or real order
We provide the solution of nonhomogeneous fractional integral equations of the form
Summary
Fractional calculus is the theory of derivatives and integrals of arbitrary complex or real order. Morita [6] studied the initial value problem of fractional differential equations by using the Laplace transform. As a result, he obtained the solutions to the fractional. I02σ+ y(t) + a · I0σ+ y(t) + b · y(t) = f (t), where I0σ+ is the Riemann–Liouville fractional integral of order σ = 1/2, 1, f (t) = tn , tn et , n ∈ N ∪ {0}, t ∈ R+ , and a, b are constants, by using the Laplace transform technique They obtained solutions in the form of Mellin–Ross functions and of exponential functions.
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