YUKLANGAN TO'LQIN-DIFFUZIYA TENGLAMASI UCHUN TO'XTAB YETISHTIRISH SHARTI BILAN MAHALLIY BO'LMAGAN MASALAL. KASRLI HOSILANI O'Z ICHIGA OLADI.
Annotatsiya
Ushbu ishda Rimann-Liuvill kasr hosilasi ishtirokidagi yuklangan
parabolik-giperbolik tenglama uchun uzlukli ulash shartli nolokal chegaraviy masala
yechimining mavjudligi va yagonaligi o‘rganildi. Yechimning yagonaligi integral energiya
usuli bilan, mavjudligi esa integral tenglamalar usuli bilan isbotlangan.
Kalit so'zlar
Yuklangan tenglama, to'lqin-diffuziya tenglamasi, Riman-Liuville kasr hosilasi, yechimning mavjudligi va yagonaligi, lokal bo'lmagan shart, uzluksiz mos kelish sharti, integral energiya, integral tenglamalar..
Adabiyotlar ro'yxati
- K. Diethelm, A.D. Freed. On the solution of nonlinear fractional order differential
- equations used in the modeling of viscoelasticity, in: F. Keil,W. Mackens, H. Voss, J. Werther (Eds.),
- Scientific Computing in Chemical Engineering II—Computational Fluid Dynamics, Reaction
- Engineering and Molecular Properties, Springer-Verlag, Heidelberg.(1999), pp. 217–224.
- [2] B.N. Lundstrom, M.H. Higgs, W.J. Spain, A.L. Fairhall. Fractional differentia-tion by
- neocortical pyramidal neurons, Nat. Neurosci. 11 (2008) 1335–1342.
- [3] W.G. Glockle, T.F. Nonnenmacher. A fractional calculus approach of self-similar protein
- dynamics, Biophys. J. 68 (1995) 46–53.
- [4] R. Hilfer. Applications of Fractional Calculus in Physics, World Scientific, Singapore,
- (2000).
- [5] F. Mainardi. Fractional calculus: some basic problems in continuum and statistical
- mechanics, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum
- Mechanics, Springer-Verlag, Wien.(1997), pp. 291–348.
- [6] J.W. Kirchner, X. Feng, C. Neal. Fractal streamchemistry and its implications for
- contaminant transport in catchments, Nature 403 (2000) 524–526.
- [7] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo. Theory and Applications of Fractional
- Differential Equations, in: North-Holland Mathematics Studies, vol. 204,
- Elsevier Science B.V., Amsterdam. (2006).
- [8] K.S. Miller, B. Ross. An Introduction to the Fractional Calculus and Differential Equations,
- John Wiley, New York, (1993).
- [9] S.G. Samko, A.A. Kilbas, O.I. Marichev. Fractional Integral and Derivatives: Theory and
- Applications, Gordon and Breach, Longhorne, PA, (1993).
- [10] I. Podlubny. Fractional Differential Equations, Academic Press, New York, (1999).
- [11]. V. Lakshmikantham and A. S. Vatsala. Basic theory of fractional di®erential equations.
- Nonlinear Anal. 69(2008), No. 8, 2677-2682.
- [12]. V. Lakshmikantham and A. S. Vatsala. Theory of fractional di®erential inequalities and
- applications. Commun. Appl. Anal. 11(2007), No. 3-4, 395-402.
- [13]. A. Belarbi, M. Benchohra, A. Ouahab. Uniqueness results for fractional functional
- differential equations with infinite delay in Frechet spaces. Appl. Anal. 85(2006),No. 12, 1459-1470.
- [14]. M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab. Existence results for fractional
- order functional differential equations with infinite delay. J. Math. Anal.Appl. 338(2008), No. 2, 1340-
- 1350.
- [15]. I. Podlubny. Geometric and physical interpretation of fractional integration and
- fractional differentiation. Dedicated to the 60th anniversary of Prof. Francesco Mainardi. Fract. Calc.
- Appl. Anal. 5(2002), No. 4, 367-386.
- [16].A. A. Kilbas., O. A. Repin. “An analog of the Tricomi problem for a mixed type equation
- with a partial fractional derivative,” Fractional Calculus & Applied Analysis. (2010) v
Yuklab olishlar
Yuklab olish ma’lumotlari hali mavjud emas.