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- Title
Solution of Inhomogeneous Fractional Differential Equations with Polynomial Coefficients in Terms of the Green's Function, in Nonstandard Analysis.
- Authors
Morita, Tohru; Sato, Ken-ichi
- Abstract
Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green's function, in the framework of distribution theory. In the present paper, a compact recipe in nonstandard analysis is presented, which is applicable to an inhomogeneous ordinary and also fractional differential equation with polynomial coefficients. The recipe consists of three theorems, each of which provides the particular solution of a differential equation for an inhomogeneous term, satisfying one of three conditions. The detailed derivation of the applications of these theorems is given for a simple fractional differential equation and an ordinary differential equation.
- Subjects
FRACTIONAL differential equations; NONSTANDARD mathematical analysis; DIFFERENTIAL equations; POLYNOMIALS; GREEN'S functions; MATHEMATICS
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 16, p1944
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9161944