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

Author

Listed:
  • Tohru Morita

    (Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan)

  • Ken-ichi Sato

    (College of Engineering, Nihon University, Koriyama 963-8642, Japan)

Abstract

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivative (fD) and the distribution theory in the space D′ R or the AC of Laplace transform. We now obtain the solutions of the hypergeometric DE, which are expressed by the hypergeometric functions, with the aid of the AC of Riemann–Liouville fD, and the distribution theory in the space D′ r,R , which is introduced in this paper, or by the term-by-term inverse Laplace transform of AC of Laplace transform of the solution expressed by a series.

Suggested Citation

  • Tohru Morita & Ken-ichi Sato, 2016. "Solution of Differential Equations with Polynomial Coefficients with the Aid of an Analytic Continuation of Laplace Transform," Mathematics, MDPI, vol. 4(1), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:1:p:19-:d:65941
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