  In this research paper, we provide a concise overview of fractal calculus
applied to fractal sets. We introduce and solve a second $\alpha$-order fractal
differential equation with constant coefficients across different scenarios. We
propose a uniqueness theorem for second $\alpha$-order fractal linear
differential equations. We define the solution space as a vector space with
non-integer orders. We establish precise conditions for second $\alpha$-order
fractal linear differential equations and derive the corresponding fractal
adjoint differential equation.
