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

Tohru Morita and Ken-ichi Sato
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Tohru Morita: Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan
Ken-ichi Sato: Kurume Library on Mathematics, Koriyama 963-8846, Japan

Mathematics, 2020, vol. 8, issue 12, 1-17

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.

Keywords: linear differential equations with polynomial coefficients; Euler’s differential equation; distribution theory; fractional calculus; nonstandard analysis; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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