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 AM  Vol.4 No.11 A , November 2013
Remarks on the Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type
Tohru Morita, Ken-ichi Sato
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Abstract: We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation.
Keywords: Laplace’s Differential Equation; Kummer’s Differential Equation; Fractional Differential Equation; Inhomogeneous Equation; Distribution Theory; Operational Calculus
Cite this paper: 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. 11, 2013, pp. 13-21. doi: 10.4236/am.2013.411A1003.
References

[1]   K. Yosida, “The Algebraic Derivative and Laplace’s Differential Equation,” Proceedings of the Japan Academy, Vol. 59, Ser. A, 1983, pp. 1-4.

[2]   K. Yosida, “Operational Calculus,” Springer-Verlag, New York, 1982, Chapter VII.

[3]   J. Mikusiński, “Operational Calculus,” Pergamon Press, London, 1959.

[4]   T. Morita and K. Sato, “Solution of Fractional Differential Equation in Terms of Distribution Theory,” Interdisciplinary Information Sciences, Vol. 12, No. 2, 2006, pp. 71-83.

[5]   T. Morita and K. Sato, “Neumann-Series Solution of Fractional Differential Equation,” Interdisciplinary Information Sciences, Vol. 16, 2010, pp. 127-137.

[6]   M. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables,” Dover Publ. Inc., New York, 1972, Chapter 13.

[7]   M. Magnus and F. Oberhettinger, “Formulas and Theorems for the Functions of Mathematical Physics,” Chelsea Publ. Co., New York, 1949, Chapter VI.

 
 
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