Applications of Fractal Interpolation in Mathematical Functions
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".
Deadline for manuscript submissions: 31 July 2026 | Viewed by 12
Special Issue Editors
Interests: fractal interpolation; iterated function systems; fixed point theory
Interests: efficient representations of multidimensional data via frames, wavelets, and fractals; abstract and applied harmonic analysis; functional analysis; wavelets, splines, and frames; approximation and interpolation theory; fractal analysis and fractal geometry
Special Issue Information
Dear Colleagues,
In recent years, fractal interpolation has gained increasing interest in the research community, especially as a powerful tool for approximating complex, irregular, and self-similar phenomena observed across various scientific fields. Unlike classical interpolation techniques, fractal interpolation functions (FIFs) incorporate self-similarity and nonlinearity, making them especially suitable for modeling real world data with intricate or fragmented structures. A defining characteristic of FIFs is that they are continuous but may not be differentiable at every point, allowing them to capture the irregularities seen in natural phenomena more effectively. The spectrum of fractal interpolants ranges from those that are nowhere differentiable to those that are infinitely differentiable, offering a broad range of applications in both theoretical and practical contexts.
This Special Issue aims to gather original research and comprehensive reviews on the theory, development, and applications of fractal interpolation methods. Topics of interest include, but are not limited to, novel construction techniques for FIFs, hidden variable FIFs, multifractal and self-affine interpolants, convergence and stability analysis, and applications in machine learning, signal processing, image analysis, data fitting, and the solution of differential equations, among others. We also encourage submissions that explore interdisciplinary applications where fractal-based interpolation methods provide advantages over traditional approaches. This Special Issue welcomes theoretical advancements, computational methods, and studies that highlight the utility and versatility of fractal interpolation in mathematical modeling. Contributions from both academia and industry are welcome.
Dr. Cristina Pacurar
Prof. Dr. Peter Massopust
Guest Editors
Manuscript Submission Information
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Keywords
- fractal interpolation functions (FIFs)
- fractal functions and surfaces
- iterated function systems (IFS)
- self-similarity and nonlinearity
- self-affine and self-conformal structures
- fractal approximation and modeling
- function approximation
- irregular and complex data modeling
- signal and image processing
- data fitting and curve reconstruction
- mathematical and computational algorithms
- applications in engineering, finance, biology, and natural sciences
- multifractal analysis
- function spaces and interpolation theory
- fractal geometry in applied mathematics
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