This paper introduces a novel fixed-point framework for orbital contractions within the setting of JS-metric spaces endowed with directed graphs. By relaxing conventional metric conditions and incorporating graph-theoretical structures, we define a new class of operators known as orbitally $\mathcal{O}$-transitive edge-preserving mappings. Utilizing an adaptive control function class $H\left(X\right)$, we establish sufficient conditions for the existence of fixed points that are specifically tailored to the iterative paths generated by the mappings. The theoretical results are supported by concrete examples demonstrating that our proposed framework strictly generalizes traditional edge-preserving properties. Furthermore, we illustrate the broad applicability and practical significance of our abstract theorems by establishing existence criteria for two major problems: nonlinear integral equations and nonlinear fractional differential equations involving Riemann–Liouville fractional derivatives with nonlocal integral boundary conditions. By reformulating these boundary value problems into equivalent Volterra-type integral equations, we show that our graph-based contraction approach is highly effective in both classical and fractional analytical settings.

Upper Northern Thailand is a critical region reflecting the severity of seasonal PM2.5 pollution and its transboundary spread, yet accurate spatial monitoring remains difficult due to complex mountainous terrain and a sparse network of physical monitoring stations. To resolve this observational limitation under a fixed sensor budget, this study develops a multi-criteria spatial optimization framework using weighted-sum scalarization to identify optimal locations for network expansion. We integrate set-dependent geostatistical Average Kriging Variance (AKV) reduction, meteorological correlation graphs, and cross-source satellite discrepancy into a unified combinatorial objective. Feature selection reveals that coupling rainfall, relative humidity, and temperature yields the best predictive performance, achieving an $R^2$ of 0.8785 and minimizing RMSE to $33.91\mathsf{\mu }{\mathrm{g}/\mathrm{m}}^3$ under Universal Kriging (UK). While Ordinary Kriging (OK) and Universal Kriging produce consistent spatial patterns, UK systematically secures superior variance reduction by accounting for coordinate-based spatial trends. Comparing optimization algorithms demonstrates distinct search dynamics: Genetic Algorithms (GAs) converge faster for smaller network expansion sizes, whereas Simulated Annealing (SA) becomes more scalable and efficient when adding 20 or more stations. Incorporating graph centrality measures (betweenness centrality and clustering coefficient) actively promotes spatial dispersion and prevents candidate stations from clustering redundantly in high-uncertainty areas. Furthermore, retrospective ground-station masking experiments demonstrate that the framework reliably targets genuine observational blind spots, reducing out-of-sample prediction RMSE by up to 40.98% upon network expansion. The proposed framework provides a practical, data-driven decision-support screening tool for environmental agencies seeking cost-effective air quality infrastructure expansion in data-sparse regions.