Solution of Euler’s Differential Equation and AC-Laplace Transform of Inverse Power Functions and Their Pseudofunctions, in Nonstandard Analysis
Journal of Advances in Mathematics and Computer Science · pp. 47–60 · Published 10 Mar 2021
10.9734/jamcs/2021/v36i130329Abstract
It is shown that the index law of the Riemann-Liouville fractional derivative is recovered when nonstandard analysis is applied, and then the solutions of Euler’s differential equation are obtained in nonstandard analysis, where infinitesimal number appears. They are given in the form, from which the solutions in distribution theory are obtained. In the derivation, the AC-Laplace transforms of functions tν and tν(loge t) m for complex number ν and positive integer m, are used. By using these formulas, the AC-Laplace transforms of functions t− n + and t− n +(loge t) m for positive integers n and m, and their pseudofunctions are obtained with the aid of nonstandard analysis.
References (2)
- 1 Theorie des distributions
- 2 The solution of Euler-Cauchy equation using Laplace transform [DOI]
Cited by 5
Tohru Morita, Ken-ichi Sato · Mathematics · 2021
Tohru Morita · AppliedMath · 2022
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