<p>This work is devoted to an inverse and direct problems with the Dirichlet boundary condition for a loaded fractional-order diffusion equation with involution perturbation. The existence and uniqueness theorem of solutions to the formulated problem is proved. The solution is obtained in the form of a series expansion using a set of appropriate orthogonal bases. The convergence of the obtained solution is also proved. The necessary classes of given functions are identified to ensure the existence and uniqueness of a solution to the inverse and direct problems with Dirichlet boundary conditions.</p>