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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 71–81 (Mi ufa134)  

This article is cited in 18 scientific papers (total in 18 papers)

Symmetry properties for systems of two ordinary fractional difeferential equations

A. A. Kasatkin

Ufa State Aviation Technical University, Ufa, Russia

Abstract: Lie point symmetries of two systems of ordinary fractional differential equations with the Riemann–Liouville derivatives are considered. Infinite algebra $L$ of equivalence transformation operators is constructed. It is shown that all admitted operators generate some subalgebra in $L$ and classification of systems with respect to point symmetries can be based on the optimal system of subalgebras. The optimal system of one-dimensional $L$ subalgebras and the complete normalized optimal system for its finite-dimensional part $L_6$ are constructed.

Keywords: fractional derivatives, symmetries, group classification, optimal system of subalgebras.

Full text: PDF file (427 kB)
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UDC: 517.9
Received: 30.12.2011

Citation: A. A. Kasatkin, “Symmetry properties for systems of two ordinary fractional difeferential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 71–81

Citation in format AMSBIB
\Bibitem{Kas12}
\by A.~A.~Kasatkin
\paper Symmetry properties for systems of two ordinary fractional difeferential equations
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 71--81
\mathnet{http://mi.mathnet.ru/ufa134}


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    This publication is cited in the following articles:
    1. Gazizov R.K., Kasatkin A.A., “Construction of Exact Solutions for Fractional Order Differential Equations by the Invariant Subspace Method”, Comput. Math. Appl., 66:5 (2013), 576–584  crossref  mathscinet  isi  elib  scopus
    2. Jefferson G.F., Carminati J., “Fracsym: Automated Symbolic Computation of Lie Symmetries of Fractional Differential Equations”, Comput. Phys. Commun., 185:1 (2014), 430–441  crossref  isi  elib  scopus
    3. Hu Juan, Ye Yujian, Shen Shoufeng, Zhang Jun, “Lie symmetry analysis of the time fractional KdV-type equation”, Appl. Math. Comput., 233 (2014), 439–444  crossref  mathscinet  zmath  isi  elib  scopus
    4. Yu. N. Grigoriev, S. V. Meleshko, A. Suriyawichitseranee, “On group classification of the spatially homogeneous and isotropic Boltzmann equation with sources II”, International Journal of Non-Linear Mechanics, 61 (2014), 15–18  crossref  isi  elib  scopus
    5. P. Voraka, S. V. Meleshko, “Group classification of one-dimensional equations of capillary fluids where the specific energy is a function of density, density gradient and entropy”, International Journal of Non-Linear Mechanics, 62 (2014), 73–84  crossref  isi  elib  scopus
    6. Jafari H., Kadkhoda N., Baleanu D., “Fractional Lie Group Method of the Time-Fractional Boussinesq Equation”, Nonlinear Dyn., 81:3 (2015), 1569–1574  crossref  isi  elib  scopus
    7. Bakkyaraj T., Sahadevan R., “Invariant Analysis of Nonlinear Fractional Ordinary Differential Equations With Riemann-Liouville Fractional Derivative”, Nonlinear Dyn., 80:1-2 (2015), 447–455  crossref  zmath  isi  elib  scopus
    8. Suksern S., Moyo S., Meleshko S.V., “Application of Group Analysis to Classification of Systems of Three Second-Order Ordinary Differential Equations”, Math. Meth. Appl. Sci., 38:18, SI (2015), 5097–5113  crossref  mathscinet  zmath  isi  scopus
    9. Mkhize T.G., Moyo S., Meleshko S.V., “Complete Group Classification of Systems of Two Linear Second-Order Ordinary Differential Equations: the Algebraic Approach”, Math. Meth. Appl. Sci., 38:9 (2015), 1824–1837  crossref  mathscinet  zmath  isi  scopus
    10. Siriwat P., Kaewmanee C., Meleshko S.V., “Group Classification of One-Dimensional Nonisentropic Equations of Fluids With Internal Inertia II. General Case”, Continuum Mech. Thermodyn., 27:3 (2015), 447–460  crossref  mathscinet  zmath  isi  scopus
    11. Meleshko S.V., Moyo S., “On Group Classification of Normal Systems of Linear Second-Order Ordinary Differential Equations”, Commun. Nonlinear Sci. Numer. Simul., 22:1-3 (2015), 1002–1016  crossref  mathscinet  zmath  isi  scopus
    12. K. Singla, R. K. Gupta, “On Invariant Analysis of Some Time Fractional Nonlinear Systems of Partial Differential Equations. I”, J. Math. Phys., 57:10 (2016), 101504  crossref  mathscinet  zmath  isi  scopus
    13. F.-Sh. Long, A. Karnbanjong, A. Suriyawichitseranee, Yu. N. Grigoriev, S. V. Meleshko, “Application of a Lie Group Admitted By a Homogeneous Equation For Group Classification of a Corresponding Inhomogeneous Equation”, Commun. Nonlinear Sci. Numer. Simul., 48 (2017), 350–360  crossref  mathscinet  isi  scopus
    14. T. M. Garrido, A. A. Kasatkin, M. S. Bruzon, R. K. Gazizov, “Lie Symmetries and Equivalence Transformations For the Barenblatt-Gilman Model”, J. Comput. Appl. Math., 318:SI (2017), 253–258  crossref  mathscinet  zmath  isi  scopus
    15. K. Singla, R. K. Gupta, “Generalized Lie Symmetry Approach For Fractional Order Systems of Differential Equations. III”, J. Math. Phys., 58:6 (2017), 061501  crossref  mathscinet  zmath  isi  scopus
    16. H. Jafari, N. Kadkhoda, M. Azadi, M. Yaghoubi, “Group Classification of the Time-Fractional Kaup-Kupershmidt Equation”, Sci. Iran., 24:1 (2017), 302–307  crossref  isi
    17. Feng W., Zhao S., “Time-Fractional Inhomogeneous Nonlinear Diffusion Equation: Symmetries, Conservation Laws, Invariant Subspaces, and Exact Solutions”, Mod. Phys. Lett. B, 32:32 (2018), 1850401  crossref  mathscinet  isi  scopus
    18. Wang L.-zh., Wang D.-j., Shen Sh.-f., Huang Q., “Lie Point Symmetry Analysis of the Harry-Dym Type Equation With Riemann-Liouville Fractional Derivative”, Acta Math. Appl. Sin.-Engl. Ser., 34:3 (2018), 469–477  crossref  mathscinet  zmath  isi  scopus
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