Organizers: Dr. Saurabh Verma, Indian Institute of Information Technology (IIIT)Allahabad, Prayagraj, India, Dr. Rattan Lal, Punjab Engineering College (Deemed to be University), Chandigarh,India, Dr. Narendra Singh Yadav, IIIT Sri City, India
Emails: saurabhverma@iiita.ac.in, rattanlal@pec.edu.in, narendrasingh.y@iiits.in
Description: We usually see functions with high irregularity/non-smoothness in natureand finance. Approximating and studying such nonsmooth functions or data-fitting forrandom natural phenomena may be better via fractal geometry tools, such as fractalsets, fractal functions, and fractal dimensions, an active research area in mathematics.This session will focus on exploring differential equations on irregular domains with theirsolution and the construction of solutions by approximation. New tools from fractalgeometry play an essential role in that they can help us to find solutions to a differentialequation on the fractal domain and approximate a nonsmooth function while preservingcertain shape, regularity, and dimension properties. The main target of this session is tobring together scientists, including young researchers, to contribute papers in the areasof use of dimension theory, fractal functions, and measures in PDEs and NumericalApproximation.
The highlighted topics: Fractal sets and measures, Fractal interpolation, Boxdimension, Hausdorff dimension, Dimension-preserving approximation, Numericalapproximation of continuous functions using fractals, Data-driven fractal approximation,Holder functions, Nowhere-differentiable functions, Analytical and Smoothness analysis,Convergence analysis, Error analysis, Parabolic PDEs, Difference/Element/VolumeMethods on Fractal domains, Laplacians on fractal domains, Spectral Theory on Fractals.