Solution of Differential Equations with the Aid of an Analytic Continuation of Laplace Transform

Tohru Morita, Ken-ichi Sato

College of Engineering, Nihon University, Koriyama, Japan.
Tohoku University, Sendai, Japan.

DOI: 10.4236/am.2014.58115                

Abstract

We discuss the solution of Laplace’s differential equation and a fractional differential equation of that type, by using analytic continuations of Riemann-Liouville fractional derivative and of Laplace transform. We show that the solutions, which are obtained by using operational calculus in the framework of distribution theory in our preceding papers, are obtained also by the present method.

Keywords

Laplace’s Differential Equation, Kummer’s Differential Equation, Fractional Differential Equation, Laplace Transform, Analytic Continuation via Hankel’s Contour

Conflicts of Interest

The authors declare no conflicts of interest.

References

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