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)
"Symmetric Decomposition of f ∈ L2(R) Via Fractional Riemann-Liouville Operators,"
Progress in Fractional Differentiation & Applications: Vol. 6:
2, Article 7.
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol6/iss2/7