Geodesic
A priori estimate for an equation with fractional derivatives with different origins
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 29 (2019) no. 4, pp. 41-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.
Keywords: Riemann-Liouville fractional derivative, Caputo fractional derivative, boundary value problem, a priori estimate. 
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     title = {A priori estimate for an equation with fractional derivatives with different origins},
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Liana M. Èneeva. A priori estimate for an equation with fractional derivatives with different origins. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 29 (2019) no. 4, pp. 41-47. http://geodesic.mathdoc.fr/item/VKAM_2019_29_4_a4/

[1] Nakhushev A. M., Drobnoye ischisleniye i yego primeneniye, Fizmatlit, Moskva, 2003, 272 pp., (in Russian)

[2] Rekhviashvili S. SH., “Formalizm Lagranzha s drobnoy proizvodnoy v zadachakh mekhaniki”, Pis'ma v ZHTF, 30:2 (2004), 33–37, (in Russian)

[3] Rekhviashvili S. SH., “K opredeleniyu fizicheskogo smysla drobnogo integro-differentsirovaniya”, Nelineynyy mir, 5:4 (2007), 194–197, (in Russian)

[4] Stanković B., “An equation with left and right fractional derivatives”, Publications de l’institut mathématique. Nouvelle série,, 80(94) (2006), 259–272 | DOI | MR | Zbl

[5] Atanackovic T. M., Stankovic B., “On a differential equation with left and right fractional derivatives”, Fractional Calculus and Applied Analysis, 10:2 (2007), 139–150 | MR | Zbl

[6] Torres C., “Existence of a solution for the fractional forced pendulum”, Journal of Applied Mathematics and Computational Mechanics, 13:1 (2014), 125–142 | DOI

[7] Eneyeva L. M., “Krayevaya zadacha dlya differentsial'nogo uravneniya s proizvodnymi drobnogo poryadka s razlichnymi nachalami”, Vestnik KRAUNTS. Fiz.-mat. nauki, 3:2(11) (2015), 39–44, (in Russian)

[8] Tokmagambetov N., Torebek B. T., “Fractional Analogue of Sturm-Liouville Operator”, Documenta Mathematica, 21 (2016), 1503–1514 | MR | Zbl

[9] Eneyeva L. M., “Otsenka pervogo sobstvennogo znacheniya zadachi Dirikhle dlya obyknovennogo differentsial'nogo uravneniya s proizvodnymi drobnogo poryadka s razlichnymi nachalami”, Izvestiya KBNTS RAN, 2017, no. 1(75), 34–40, (in Russian)

[10] Eneyeva L. M., “O zadache Neymana dlya uravneniya s drobnymi proizvodnymi s razlichnymi nachalami”, Vestnik KRAUNTS. Fiz.-mat. nauki., 2018, no. 4(24), 61–65, (in Russian) | MR | Zbl

[11] Eneyeva L. M., “Nervayenstvo Lyapunova dlya uravneniya s proizvodnymi drobnogo poryadka s razlichnymi nachalami”, Vestnik KRAUNTS. Fiz.-mat. nauki., 2019, no. 3(28), 32–49, (in Russian) | MR

[12] Eneeva L.M., Pskhu A.V., Potapov A.A., Feng T., Rekhviashvili S.Sh., “Lyapunov inequality for a fractional differential equation modeling damped vibrations of thin film MEMS”, Advances in Intelligent Systems and Computing. ICCD2019 (paper ID: E19100), 2019

[13] Rekhviashvili S.Sh., Pskhu A.V., Potapov A.A., Feng T., Eneeva L.M., “Modeling damped vibrations of thin film MEMS”, Advances in Intelligent Systems and Computing. ICCD2019 (paper ID: E19101), 2019

[14] George A. Anastassiou, “Fractional representation formulae and right fractional inequalities”, Mathematical and Computer Modelling, 2011, no. 54, 3098–3115 | MR | Zbl

[15] George A. Anastassiou, Fractional Differentiation Inequalities, Springer-Verlag, New York, 2009, 675 pp. | MR | Zbl