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Solution of Euler’s Differential Equation in Terms of Distribution Theory and Fractional Calculus

Author

Listed:
  • Tohru Morita

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

  • Ken-ichi Sato

    (Kurume Library on Mathematics, Koriyama 963-8846, Japan)

Abstract

For Euler’s differential equation of order n , a theorem is presented to give n solutions, by modifying a theorem given in a recent paper of the present authors in J. Adv. Math. Comput. Sci. 2018; 28(3): 1–15, and then the corresponding theorem in distribution theory is given. The latter theorem is compared with recent studies on Euler’s differential equation in distribution theory. A supplementary argument is provided on the solutions expressed by nonregular distributions, on the basis of nonstandard analysis and Laplace transform.

Suggested Citation

  • Tohru Morita & Ken-ichi Sato, 2020. "Solution of Euler’s Differential Equation in Terms of Distribution Theory and Fractional Calculus," Mathematics, MDPI, vol. 8(12), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2117-:d:451452
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