We study the topology and fixed point theory of soft b-metric spaces. In contrast to the soft metric case, we show by an explicit example that, when s > 1, a soft open ball need not be open in the induced topology τd, which indicates a genuine divergence between the ball structure and τd. We also discuss compactness-related consequences of this mismatch between ball covers and τd-open covers. On the fixed point side, we establish existence and uniqueness results for Reich– Ćirić-type contractions and for a rational-type contractive condition in complete soft b-metric spaces together with an α–ψ extension. As applications, we obtain solvability of a class of soft integral equations and of a Caputo fractional boundary value problem via an associated integral operator. Finally, we provide an explicit iterative scheme for rational contractions and a brief computational illustration in comparison with a standard linear contraction.
This work is licensed under a Creative Commons Attribution 4.0 International License.