TITLE:
Solution of Differential Equations with the Aid of an Analytic Continuation of Laplace Transform
AUTHORS:
Tohru Morita, Ken-ichi Sato
KEYWORDS:
Laplace’s Differential Equation, Kummer’s Differential Equation, Fractional Differential Equation, Laplace Transform, Analytic Continuation via Hankel’s Contour
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.8,
May
8,
2014
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.