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Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type
Tohoku University, Sendai, Japan
College of Engineering, Nihon University, Koriyama, Japan
- 1 Tohoku University, Sendai, Japan
- 2 College of Engineering, Nihon University, Koriyama, Japan
Applied Mathematics·Volume 04 (2013)·Pages 26–36·Published 16 October 2013·DOI10.4236/am.2013.411A1005
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Abstract
In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.
KeywordsLaplace’s Differential EquationKummer’s Differential EquationFractional Differential EquationDistribution TheoryOperational CalculusInhomogeneous EquationPolynomial Solution
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