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• Talk 01 — Guru Prem Prasad M (Indian Institute of Technology Guwahati, India) — [computing…]
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  Title: Dynamics of One Parameter Family of Entire Functions involving Hyperbolic Cosine Function
  Abstract

  The one parameter family of transcendental entire functions $f_{\lambda}(z)=\lambda + z +\cosh z$ for $z\in\mathbb{C}$, $\lambda \in \mathbb{R}$ that has an unbounded set of singular values is considered. We first explore the real dynamics of $f_{\lambda}$ for different ranges of parameter values and prove the existence of period doubling bifurcation for $ \lambda =-\sqrt{5}$. It is proved that the Fatou set $\mathcal{F}(f_{\lambda})$ contains parabolic domains and its preimages for $\vert \lambda \vert =1$ or $\sqrt{5}$; and attracting domains and its preimages for $1< \vert\lambda \vert<\sqrt{5}$. Further, we establish that $\mathcal{F}(f_{\lambda})$ is empty for $\vert \lambda \vert <1$.

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• Talk 02 — Pasupathi R (National Institute of Technology Agartala, India) — [computing…]
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  Title: Fractal Interpolation Functions via Weak Contractions
  Abstract

  This talk focuses on a generalized framework for fractal interpolation functions originally introduced by Michael Barnsley. The classical construction based on Banach contractions is extended by considering Edelstein contractions in the second variable, thereby incorporating broader classes such as Matkowski, Meir–Keeler, F-contractions, and θ-contractions. The presentation highlights how this generalized approach provides greater flexibility in constructing fractal interpolation functions and discusses estimates for the lower and upper box dimensions of their graphs.

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• Talk 03 — Alireza Khalili Golmankhaneh (Ur. C., Islamic Azad University, Iran) — [computing…]
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  Title: Fractal Calculus: From Mathematical Foundations to Physical Modeling
  Abstract

  Fractal structures arise naturally in a wide variety of physical, biological, and engineering systems, including porous media, turbulent flows, polymer chains, percolation clusters, anomalous diffusion, and complex transport phenomena. However, the irregular and non-differentiable nature of fractals makes the methods of ordinary calculus inadequate for describing dynamics on such geometries. Fractal calculus provides a mathematical framework specifically designed for analysis on fractal sets and fractal curves.
  
  In this talk, we present the foundations of F(α)-calculus, a local calculus defined on fractal subsets of the real line and on fractal curves. The theory introduces new notions of integration and differentiation adapted to sets of non-integer dimension through the concepts of mass functions and staircase functions. Unlike classical fractional calculus, the resulting operators are local and their order is directly related to the dimension of the underlying fractal geometry.
  
  We discuss the formulation of F(α)-integrals and F(α)-derivatives, their conjugacy with ordinary calculus, and analogues of the fundamental theorems of calculus. The talk further highlights applications of fractal calculus in modeling physical processes on fractal media, including anomalous diffusion, fractal-time dynamical systems, Fokker–Planck equations on fractal curves, and Langevin dynamics in disordered environments.
  
  The presented framework offers a direct and algorithmic approach for constructing differential equations on fractal geometries and provides new tools for studying transport, stochastic processes, and dynamics in complex systems with intrinsic fractal structure.

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• Talk 04 — Maria Rosaria Lancia (Sezione di Matematica, Universita' di Roma Sapienza, Rome, Italy) — [computing…]
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  Title: On some inverse problems in fractal domains
  Abstract

  We consider inverse problems in an irregular domain Ω and in suitable approximating domains Ωn, for n ∈ N, respectively. After proving well-posedness results, we prove that the solutions of the approximating problems converge in a suitable sense to the solution of the problem on Ω via Mosco
  convergence. We also present some applications. These results are in collaboration with S.Creo, G.Mola and S.Romanelli.

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• Talk 05 — Vijay (Transilvania University of Brasov, Romania) — [computing…]
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  Title: Floral Designs via ZFB Curves
  Abstract

  Floral pattern generation using mathematical curve models has important applications in geometric design and computer graphics. This talk focuses on floral design generation using a fractal-based curve framework, referred to as ZFB (zipper fractal B\'ezier) curves. The construction is based on zipper $\alpha$-fractal polynomials corresponding to Bernstein basis functions. Using this framework, a variety of floral-like structures with rich geometric features can be generated.

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• Talk 06 — Abhijeet Das (Department of Bio-Engineering, Indian Institute of Science, Bangalore, India) — [computing…]
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  Title: Decoupling of spatial scales in breast pathology reveals emergent fractal-like nuclear organization from tissue spatial architecture
  Abstract

  The fractality of nuclear architecture offers a geometrically principled yet underexplored lens for quantitatively characterizing breast pathological progression. Here, we apply fractal analysis to nuclear spatial organization across the full spectrum of breast pathological progression, from normal epithelium through invasive carcinoma, spanning seven pathological categories with over 4000 regions of interest. Two complementary fractal descriptors were computed: the Correlation Dimension, a measure of nuclear spatial density, and the Minkowski Dimension, a measure of boundary morphological complexity, together constituting a multiscale geometric feature set. Power-law scaling analysis confirmed robust fractal-like behavior for both dimensions across all pathologies. Non-parametric group comparison and effect size estimation revealed significant pathology-dependent variation in both descriptors, with notably low shared variance between them, validating their geometric complementarity. A particularly striking finding was a geometric anomaly at the intermediate (flat epithelial atypia) stage, which occupied a non-monotonic position in the progression landscape, dissociated in its global versus local fractal signatures relative to adjacent pathological categories. Intraclass correlation and heterogeneity analysis further revealed substantial within-patient spatial variability, especially in mixed-pathology cases, with implications for sampling strategies in clinical biopsy. Receiver operating characteristic analysis and multi-class machine learning classification demonstrated that combining both fractal descriptors meaningfully improves discriminability across pathological transitions. However, standalone performance remains insufficient for independent clinical diagnosis. This work establishes a proof-of-concept framework demonstrating that the fractality of nuclear architecture constitutes a quantitative geometric signature of breast pathological progression, with promise as a biologically interpretable constraint for multiscale computational modeling.

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• Talk 07 — Saurabh Kumar Katiyar (Dr B R Ambedkar National Institute of Technology Jalandhar, India) — [computing…]
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  Title: A New Class of Zipper Rational Quintic Spline Fractal Interpolation Function and its Constrained Aspects
  Abstract

  This research work focuses on the area of shape preservation and establishes a theoretical framework for maintaining the constrained characteristics of prescribed data within fractal interpolation function (FIF) techniques. We construct a novel class of zipper rational quintic spline fractal interpolation functions (ZRQSFIFs) possessing a preassigned quadratic denominator involving a single shape parameter. The convergence behavior of the proposed ZRQSFIF toward the original function in $\mathcal{C}^2$ is analyzed. The scaling factors and shape parameter play a controllable role in determining the shape of the resulting curves. The components of the zipper iterated function system (IFS) on each subinterval are appropriately chosen so that the graph of the resulting $\mathcal{C}^2$-ZRQSFIF remains (i) positive, (ii) within a prescribed rectangle, (iii) above a prescribed straight line, (iv) monotonic, and (v) convex. Several numerical examples are included to demonstrate the accuracy and effectiveness of the proposed scheme and to illustrate its advantages over the corresponding classical methods.

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• Talk 08 — Mohit Kumar (VIT Chennai, India) — [computing…]
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  Title: Recurrent Fractal Interpolation Functions with Variable Scaling Parameters under Student's t-Distributed Noise
  Abstract

  Fractal interpolation functions are widely used to model irregular and self-similar data. In this study, we develop recurrent fractal interpolation functions with variable scaling parameters for two-dimensional datasets contaminated by Student’s t-distributed noise in the ordinate. Our approach enables the estimation of missing values in such noisy datasets and quantifies the uncertainty associated with these estimates. The effectiveness of the proposed method is demonstrated through a comprehensive simulation study.

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• Talk 09 — Aiswarya T (Indian Institute of Technology Tirupati, India) — [computing…]
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  Title: Nonlinear Fractal Histopolation Functions: A New Class of Fractal Approximation Functions
  Abstract

  A novel method for constructing a nonlinear fractal histopolation function associated with a given histogram is introduced in this talk. In contrast to classical fractal interpolation methods, which produce continuous and interpolatory functions, the proposed approach constructs a bounded, Riemann integrable function that is not necessarily continuous but preserves the area of a given histogram. An iterated function system based on Rakotch contractions- a generalisation of Banach contractions- is utilised, thereby extending the theoretical framework for fractal histopolation. Unlike previous formulations, the proposed construction of nonlinear fractal functions allows vertical scaling factors greater than one. The conditions for the nonlinear fractal function to be a solution for the histopolation problem are derived.

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• Talk 10 — Harsha Gopalakrishnan (Indian Institute of Technology Tirupati, India) — [computing…]
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  Title: Some Analytic and Geometric Aspects of Sequential Labyrinth Fractals
  Abstract

  Labyrinth fractals form an interesting class of post-critically finite fractals with rich analytic, geometric, and topological structures. In this talk, we discuss classical labyrinth fractals and sequential labyrinth fractals as a generalization of them. We consider sequential labyrinth fractals generated by two sequences of tuples and examine some of their fundamental properties. In particular, we study several geometric characteristics of these fractals, including the box-counting dimension and bounds for the Hausdorff dimension of the limiting fractal. We also discuss certain topological properties arising from their construction. Motivated by the post-critically finite nature of labyrinth fractals, we further investigate analytic structures on specific labyrinth fractals through the study of energy forms. In particular, we obtain a class of energy forms on a particular labyrinth fractal and derive the corresponding harmonic extension matrices associated with these energy forms. These investigations illustrate the close relationship between the analytic behaviour and geometric structure of labyrinth fractals.

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