Gazizov, R. K.; Kasatkin, A. A. Construction of exact solutions for fractional order differential equations by the invariant subspace method. (English) Zbl 1348.34012 Comput. Math. Appl. 66, No. 5, 576-584 (2013). Summary: The invariant subspace method for constructing particular solutions is modified for fractional differential equations. It allows one to reduce a fractional partial differential equation to a system of nonlinear ordinary fractional differential equations. Point symmetries of such systems are used to construct their solutions which generate solutions of the original fractional partial differential equation. Cited in 1 ReviewCited in 59 Documents MSC: 34A08 Fractional ordinary differential equations 34C14 Symmetries, invariants of ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 35R11 Fractional partial differential equations Keywords:fractional differential equations; transformation; invariance; integration PDFBibTeX XMLCite \textit{R. K. Gazizov} and \textit{A. A. Kasatkin}, Comput. Math. Appl. 66, No. 5, 576--584 (2013; Zbl 1348.34012) Full Text: DOI References: [1] Uchaikin, V. V., Method of Fractional Derivatives (2008), Artishok: Artishok Ulyanovsk, (in Russian) [2] Podlubny, I., Fractional Differential Equations (1999), Academic Press: Academic Press San Diego, New York, London · Zbl 0918.34010 [3] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., (Theory and Applications of Fractional Differential Equations. Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies (2006), Elsevier Science & Tech.: Elsevier Science & Tech. Amsterdam) · Zbl 1092.45003 [4] Baleanu, D.; Diethelm, K.; Scalas, E.; Trujillo, J. J., (Fractional Calculus Models and Numerical Methods. Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos (2012), World Scientific) · Zbl 1248.26011 [5] Buckwar, E.; Luchko, Y., Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations, Journal of Mathematical Analysis and Applications, 227, 81-97 (1998) · Zbl 0932.58038 [6] Gazizov, R. K.; Kasatkin, A. A.; Lukashchuk, S. Y., Continuous transformation groups of fractional differential equations, Vestnik USATU, 9, 21, 125-135 (2007) [7] Gazizov, R. K.; Kasatkin, A. A.; Lukashchuk, S. Y., Symmetry properties of fractional diffusion equations, Physica Scripta T, 136, 014016 (2009) [8] Ibragimov, N., Elementary Lie Group Analysis and Ordinary Differential Equations, Mathematical Methods in Practice (1999), Wiley · Zbl 1047.34001 [9] Galaktionov, V.; Svirshchevskii, S., (Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics. Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series (2007), Chapman & Hall/CRC) · Zbl 1153.35001 [10] Samko, S.; Kilbas, A.; Marichev, O., Fractional Integrals and Derivatives: Theory and Applications (1993), Gordon and Breach Science Publishers: Gordon and Breach Science Publishers Yverdon · Zbl 0818.26003 [11] Kasatkin, A. A., Symmetry properties for systems of two ordinary fractional differential equations, Ufa Mathematical Journal, 4, 1, 71-81 (2012) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.