Ashurov, RavshanCabada Fernández, AlbertoTurmetov, Batirkhan2026-02-052026-02-052016-03-09Ashurov, R., Cabada, . & Turmetov, B. Operator Method for Construction of Solutions of Linear Fractional Differential Equations with Constant Coefficients. FCAA 19, 229–252 (2016). https://doi.org/10.1515/fca-2016-00131311-0454https://hdl.handle.net/10347/45687This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1515/fca-2016-0013One of the effective methods to find explicit solutions of differential equations is the method based on the operator representation of solutions. The essence of this method is to construct a series, whose members are the relevant iteration operators acting to some classes of sufficiently smooth functions. This method is widely used in the works of B. Bondarenko for construction of solutions of differential equations of integer order. In this paper, the operator method is applied to construct solutions of linear differential equations with constant coefficients and with Caputo fractional derivatives. Then the fundamental solutions are used to obtain the unique solution of the Cauchy problem, where the initial conditions are given in terms of the unknown function and its derivatives of integer order. Comparison is made with the use of Mikusinski operational calculus for solving similar problemsengLinear fractional differential equations with constant coefficientsCaputo derivativesFundamental solutionsCauchy problem1202 Análisis y análisis funcionaljournal article10.1515/fca-2016-00131314-2224open access