"Symmetric Decomposition of f ∈ L2(R) Via Fractional Riemann-Liouville " by Yulong Li

Progress in Fractional Differentiation & Applications

Article Title

Symmetric Decomposition of f ∈ L2(R) Via Fractional Riemann-Liouville Operators

Authors

Yulong Li, Science and Mathematics, Singapore University of Technology and Design, 8 Somapah Road Singapore 487372, Singapore\\ Department of Mathematics and Statistics, University of Wyoming, 1000 E. University Avenue, Dept. 3036, Laramie, Wyoming, USA Follow

Author Country (or Countries)

USA

Abstract

The present paper proves that given −1/2 < s < 1/2, for any f ∈ L2(R), there is a unique u ∈ H􏰓|s|(R) such that f = D−su+Ds∗u, where D−s , Ds∗ are fractional Riemann-Liouville operators and the fractional derivatives are understood in the weak sense. Furthermore, regularity of u is addressed, and other versions of the results are established. Consequently, the Fourier transform of elements of L2(R) is characterized.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/060207

Recommended Citation

Li, Yulong (2020) "Symmetric Decomposition of f ∈ L2(R) Via Fractional Riemann-Liouville Operators," Progress in Fractional Differentiation & Applications: Vol. 6: Iss. 2, Article 7.
DOI: http://dx.doi.org/10.18576/pfda/060207
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol6/iss2/7

Download

COinS