When solving many fundamental and applied problems related to the study of properties of dynamical systems, situations often arise when the parameters of the model are not exactly defined. One can try to solve such a problem by searching the parameters, taking into account the understanding of the nature of the modelling process. On the other hand, it is possible to solve inverse problems—a common type of problems in many scientific fields, where it is necessary to determine the values of the model parameters on the basis of experimental data, but it is impossible to make direct measurements of the parameters. The paper considers an inhomogeneous fractional equation with a Gerasimov-Caputo type operator of variable α(t) order. The possibility of recovering the form of the function α(t) and refining its values on the basis of test generated data is investigated. The direct problem is defined as a Cauchy problem for a fractional equation solved numerically. The solution of the inverse problem is reduced to the minimization of the inviscid functional, and the minimization problem is solved using the iterative Levenberg-Marquardt unconditional optimization method. Thus, the problem of determining the optimal form α(t) of a fractional equation is reduced to 4 parameters that control the course of the solution of the inverse problem and do not depend on the physical meaning of the original problem in specific models. On test examples it was shown that the Levenberg-Marquardt method can indeed be used for unconditional optimization to determine type of function α(t) and its optimal values.