Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type

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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, “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.

[5] 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.

[6] T. Morita and K. Sato, “Neumann-Series Solution of Fractional Differential Equation,” Interdisciplinary Information Sciences, Vol. 16, No. 1, 2010, pp. 127-137.

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

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

[9] T. Morita and K. Sato, “Liouville and Riemann-Liouville Fractional Derivatives via Contour Integrals,” Fractional Calculus and Applied Analysis, Vol. 16, No. 3, 2013, pp. 630-653.

[10] L. Levine and R. Maleh, “Polynomial Solutions of the Classical Equations of Hermite, Legendre and Chebyshev,” International Journal of Mathematical Education in Science and Technology, Vol. 34, 2003, pp. 95-103.

[11] F. Riesz and B. Sz.-Nagy, “Functional Analysis,” Dover Publ., Inc., New York, 1990, p. 146.