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T. Morita and K. Sato, “Remarks on the Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type,” Applied Mathematics, Vol. 4, No. 11A, 2013, pp. 13-21.

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• TITLE: Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type

  AUTHORS: Tohru Morita, Ken-ichi Sato

  KEYWORDS: Laplace’s Differential Equation; Kummer’s Differential Equation; Fractional Differential Equation; Distribution Theory; Operational Calculus; Inhomogeneous Equation; Polynomial Solution

  JOURNAL NAME: Applied Mathematics, Vol.4 No.11A, October 31, 2013

  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.