Back to Search
Start Over
An inverse problem of determining orders of systems of fractional pseudo-differential equations.
- Source :
- Fractional Calculus & Applied Analysis; Feb2022, Vol. 25 Issue 1, p109-127, 19p
- Publication Year :
- 2022
-
Abstract
- As it is known various dynamical processes can be modeled through systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces with the problem of determination of adequate orders of time-fractional derivatives in the sense of Riemann–Liouville or Caputo. This problem is qualified as an inverse problem. The correct (vector) order can be found utilizing the available data. In this paper we offer an new method of solution of this inverse problem for linear systems of fractional order pseudo-differential equations. We prove that the Fourier transform of the vector-solution U ^ (t , ξ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{U}(t, \xi)$$\end{document} evaluated at a fixed time instance, which becomes possible due to the available data, recovers uniquely the unknown vector-order of a system of governing pseudo-differential equations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13110454
- Volume :
- 25
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Fractional Calculus & Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 156255558
- Full Text :
- https://doi.org/10.1007/s13540-021-00006-y