Back to Search
Start Over
A NEW ESTIMATION OF BOX DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS.
- Source :
-
Fractals . 2024, Vol. 32 Issue 2, p1-13. 13p. - Publication Year :
- 2024
-
Abstract
- This paper establishes a linear relationship between the order of the Riemann–Liouville fractional calculus and the exponent of the Hölder condition, whether the Hölder condition is global, local, or at a single point. We propose and prove a control inequality between the Hölder derivative ( H f (x , α) as defined in Proposition 12) of a continuous function and the Hölder derivative of the Riemann–Liouville fractional calculus of this function. In addition, this paper provides a more accurate estimation of the Box dimension of the graph of the Riemann–Liouville fractional integral of an arbitrary continuous function. More specifically, it establishes the result that whenever there is a continuous function whose graph has the upper Box dimension s with 1 < s ≤ 2 , the graph of its Riemann–Liouville fractional integral of order ν , with 0 < ν < 1 , has the upper Box dimension not greater than s − (s − 1) ν. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONTINUOUS functions
*HOLDER spaces
*FRACTIONAL calculus
*FRACTIONAL integrals
Subjects
Details
- Language :
- English
- ISSN :
- 0218348X
- Volume :
- 32
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Fractals
- Publication Type :
- Academic Journal
- Accession number :
- 176387576
- Full Text :
- https://doi.org/10.1142/S0218348X2440005X