TY  - JOUR
AU  - Sajid, Mohammad
AU  - Das, Abhishikta
AU  - Kalita, Hemanta
PY  - 2025
TI  - Metric structure for Riemann-Stieltjes derivable functions on fractals and application
JO  - AIMS Mathematics
SP  - 15737
EP  - 15754
VL  - 10
IS  - 7
AB  - This article presents a metric structure of the space of all Riemann-Stieltjes derivable functions defined over a fractal subset of the real line. Within this framework, we formulate, and analyze a measure of non-compactness tailored to fractal domains. Building upon this foundation, we develop a fixed point theorem in normed linear spaces under a generalized contraction condition, thereby extending Darbo's classical results. To illustrate the applicability of our theoretical findings, we apply this framework to the analysis of a class of fractal    α-linear differential equations, particularly focusing on models that exhibit oscillatory behaviors in fractal media settings where traditional methods often fail due to the irregularity of the domain. A numerical simulation using MATLAB supports the theoretical assertions, thus demonstrating that the noncompactness-based conditions imposed on the operator        L   are sufficient to ensure convergence within the function space        D    (  ϕ  ). This approach offers novel insights into solving differential equations in non-Euclidean geometries, thereby emphasizing the interplay between metric structures, the fixed point theory, and mechanical systems in complex media.
UR  - https://doi.org/10.3934/math.2025705
DO  - 10.3934/math.2025705