Mathematical approaches to structure model problems have a significant role in expanding our knowledge in our routine life circumstances. To put them into practice, the right formulation, method, systematic representation, and formulation are needed. The purpose of introducing soft graphs is to discretize these fundamental mathematical ideas, which are inherently continuous, and to provide new tools for applying mathematical analysis technology to real-world applications including imperfect and inexact data or uncertainty. Soft rough covering models $\left(\text{briefly},\mathcal{S}\mathcal{R}\mathcal{C}\text{-Models}\right)$, a novel theory that addresses uncertainty. In this present paper, we have introduced two new concepts $\mathcal{L}\mathfrak{i}$-soft rough covering graphs ( $\mathcal{L}\mathfrak{i}$- $\mathcal{S}\mathcal{R}\mathcal{C}\mathcal{G}$s) and the concept of fixed point of such graphs. Furthermore, we looked into a some algebras that dealt with the fixed points of $\mathcal{L}\mathfrak{i}$- $\mathcal{S}\mathcal{R}\mathcal{C}\mathcal{G}$s. Applications of the algebraic structures available in covering soft sets to soft graphs may reveal new facets of graph theory.

This paper investigated the existence and stability of solutions for boundary value problems involving Caputo fractional differential equations of variable order. Unlike constant-order models, variable-order equations allow the fractional order to change over time, enabling more flexible and accurate modeling of complex systems with evolving dynamics and memory. Using Darbo's fixed point theorem and the Kuratowski measure of noncompactness, we established new existence results for solutions within a Banach space of continuous functions. Our approach treated the variable order as piecewise constant, transforming the problem into a sequence of more manageable constant-order subproblems. Furthermore, we demonstrated Ulam-Hyers stability of the solutions, ensuring that small perturbations in the system did not lead to significant deviations in the results. To validate the theoretical findings, we provided a detailed example supported by numerical simulations. These results offered a solid foundation for future applications in science and engineering where system dynamics evolve over time.