Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions
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Yong Shun Liang
Abstract
The present paper investigates fractal dimension of fractional integral of continuous functions whose fractal dimension is 1 on [0, 1]. For any continuous functions whose Box dimension is 1 on [0, 1], Riemann-Liouville fractional integral of these functions of any positive order has been proved to still be 1-dimensional continuous functions on [0, 1].
Acknowledgements
The author thanks his institution for the support, under National Natural Science Foundation of China(Grant No. 11201230), Natural Science Foundation of Jiangsu Province (Grant No. BK20161492) and the Fundamental Research Funds for the Central Universities (Grant No. 30917011340).
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Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books
- Research Paper
- Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions
- Finite-time attractivity for semilinear tempered fractional wave equations
- Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas
- Extrapolating for attaining high precision solutions for fractional partial differential equations
- Time optimal controls for fractional differential systems with Riemann-Liouville derivatives
- Inverses of generators of integrated fractional resolvent operator functions
- A variational approach for boundary value problems for impulsive fractional differential equations
- Infinitely many solutions to boundary value problem for fractional differential equations
- A semi-analytic method for fractional-order ordinary differential equations: Testing results
- Blow-up and global existence of solutions for a time fractional diffusion equation
- A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury’s identity
- Short Paper
- Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions
