Solution of Differential Equations with the Aid of an Analytic Continuation of Laplace Transform

Show more

References

[1] Yosida, K. (1983) The Algebraic Derivative and Laplace’s Differential Equation. Proceedings of Japan Academy, 59, 14.

http://dx.doi.org/10.3792/pjaa.59.1

[2] Yosida, K. (1982) Operational Calculus. SpringerVerlag, New York, Chapter VII.

[3] Morita, T. and Sato, K. (2013) Remarks on the Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type. Applied Mathematics, 4, 1321.

http://dx.doi.org/10.4236/am.2013.411A1003

[4] Morita, T. and Sato, K. (2013) Solution of Laplace’s Differential Equation and Fractional Differential Equation of That Type. Applied Mathematics, 4, 2636.

http://dx.doi.org/10.4236/am.2013.411A1005

[5] Mikusiński, J. (1959) Operational Calculus. Pergamon Press, London.

[6] Morita, T. and Sato, K. (2006) Solution of Fractional Differential Equation in Terms of Distribution Theory. Interdisciplinary Information Sciences, 12, 7183.

[7] Morita, T. and Sato, K. (2010) NeumannSeries Solution of Fractional Differential Equation. Interdisciplinary Information Sciences, 16, 127137.

http://dx.doi.org/10.4036/iis.2010.127

[8] Morita, T. and Sato, K. (2013) Liouville and RiemannLiouville Fractional Derivatives via Contour Integrals. Fractional Calculus and Applied Analysis, 16, 630653.

http://dx.doi.org/10.2478/s1354001300409

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

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

[11] Whittaker, E.T. and Watson, G.N. (1935) A Course of Modern Analysis. Cambridge U.P., Cambridge