Remarks on the Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type

Affiliation(s)

Tohoku University, Sendai, Japan.

College of Engineering, Nihon University, Koriyama, Japan.

Tohoku University, Sendai, Japan.

College of Engineering, Nihon University, Koriyama, Japan.

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.

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.

T. Morita and K. Sato, "Remarks on the Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type,"

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.

[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.