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- Title
Solution of Euler's Differential Equation in Terms of Distribution Theory and Fractional Calculus.
- Authors
Morita, Tohru; Sato, Ken-ichi
- 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.
- Subjects
EULER equations (Rigid dynamics); NONSTANDARD mathematical analysis; FRACTIONAL calculus; LINEAR differential equations; CALCULUS
- Publication
Mathematics (2227-7390), 2020, Vol 8, Issue 12, p2117
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math8122117