RT Journal Article
T1 Operator method for construction of solutions of linear fractional differential equations with constant coefficients
A1 Ashurov, Ravshan
A1 Cabada Fernández, Alberto
A1 Turmetov, Batirkhan
K1 Linear fractional differential equations with constant coefficients
K1 Caputo derivatives
K1 Fundamental solutions
K1 Cauchy problem
AB One 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 problems
PB Springer
SN 1311-0454
YR 2016
FD 2016-03-09
LK https://hdl.handle.net/10347/45687
UL https://hdl.handle.net/10347/45687
LA eng
NO Ashurov, 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-2016-0013
NO This 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-2016-0013
NO This work has been partially supported by the Ministry of Higher and Secondary Special Education of Uzbekistan under Research Grant F4-FAF010, FEDER and by Ministerio de Ciencia y Tecnología, Spain, and FEDER, Projects MTM2010-15314 and MTM2013-43014-P, and by the Ministry of Education and Science of the Republic of Kazakhstan through the project 0819/GF4
DS Minerva
RD 24 abr 2026