Non-homogeneous Linear Set-Valued Differential Equations with Variable Matrix Coefficients

We investigate the initial value problems for non-homogeneous linear differential equations whose solutions are set-valued maps taking values in the space of nonempty compact convex subsets of ${\mathbb{R}}^2$, denoted by $K_c({\mathbb{R}}^2)$. The differential formulation is based on the generalized derivative that includes the Hukuhara derivative, as well as its extensions, Bede-Gal (BG), and Plotnikov-Skripnik (PS) derivatives, and we obtain some general as well as constructive formulas for the solutions. Several illustrative examples are provided.