We would like to consider an application of generalized Laplace transform in partial differential equations(PDEs) by using the n-th partial derivatives. The tool of this research is the induction, and the proposed idea gives an easy solution to engineering problems by freely selecting the integer α in the definition.
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.
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