Asymptotic Integration of Some Classes of Fractional Differential Equations

[1] AGARWAL, R. P.-DJEBALI, S.-MOUSSAOUI, T.-MUSTAFA, O. G.: On the asymptoticintegration of nonlinear differential equations, J. Comput. Appl. Math. 202 (2007), 352-376.10.1016/j.cam.2005.11.038Search in Google Scholar

[2] BǍLEANU, D.-MUSTAFA, O. G.-AGARWAL, R. P.: Asymptotically linear solutionsfor some linear fractional differential equations, Abstr. Appl. Anal., Vol. 2010, Article ID 865139, 8 p.10.1155/2010/865139Search in Google Scholar

[3] BǍLEANU, D.-MUSTAFA, O. G.-AGARWAL, R. P.: Asymptotic integration of (1+α)-order fractional differential equatios, Comput. Math. Appl. 62 (2011), 1492-1500.10.1016/j.camwa.2011.03.021Search in Google Scholar

[4] BIHARI, I.: Researches of the boundedness and stabiliy of solutions of non-linear differentialequations, Acta Math. Acad. Hungar. 8 (1957), 261-278.10.1007/BF02020315Search in Google Scholar

[5] CALIGO, D.: Comportamento asintotico degli integrali dell’equazione y′′(x)+A(x)y(x) = = 0, nell’ipotesi limx→+∞ A(x) = 0, Boll. Un. Mat. Ital. 6 (1941), 286-295.Search in Google Scholar

[6] CAPUTO, M.: Linear models of dissipation whose Q is almost frequency independent II, Geophys. J. Royal Astronom. Soc. 13 (1967), 529-535.10.1111/j.1365-246X.1967.tb02303.xSearch in Google Scholar

[7] COHEN, D. S.: The asymptotic behavior of a class of nonlinear differntial equations, Proc. Amer. Math. Soc. 18 (1967), 607-609.10.1090/S0002-9939-1967-0212289-3Search in Google Scholar

[8] CONSTANTIN, A.: On the asymptotic behavior of second order nonlinear differentialequations, Rend. Math. Appl. 13 (1993), 627-634.Search in Google Scholar

[9] CONSTANTIN, A.: On the existence of positive solutions of second order differentialequations, Ann. Mat. Pura Appl. (4) 184 (2005), 131-138.10.1007/s10231-004-0100-1Search in Google Scholar

[10] DANNAN, F. M.: Integral inequalities of Gronwall-Bellman-Bihari type and asymptoticbehavior of certain second order nonlinear differential equations, J. Math. Anal. Appl. 108 (1985), 151-164.10.1016/0022-247X(85)90014-9Search in Google Scholar

[11] FURATI, M.-TATAR, N. E.: Power-type estimates for nonlinear fractional differentialequations, Nonlinear Anal. 62 (2001), 1025-1036.10.1016/j.na.2005.04.010Search in Google Scholar

[12] KILBAS, A. A.-SRIVASTAVA, H. M.-TRUJILLO, J. J.: Theory and Applicationsof Fractional Differential Equations, in: North-Holland Math. Stud., Vol. 204, Elsevier, Amsterdam, 2006.Search in Google Scholar

[13] KUSANO, T.-TRENCH, W. F.: Global existence of second order differential equationswith integrable coefficients, J. London Math. Soc. 31 (1985), 478-486.10.1112/jlms/s2-31.3.478Search in Google Scholar

[14] KUSANO, T.-TRENCH,W. F.: Existence of global solutions with prescribed asymptoticbehavior for nonlinear ordinary differential equations, Ann. Mat. Pura Appl. (4) 142 (1985), 381-392.10.1007/BF01766602Search in Google Scholar

[15] LIPOVAN, O.: On the asymptotic behaviour of the solutions to a class of second ordernonlinear differential equations, Glasgow Math. J. 45 (2003), 179-187.10.1017/S0017089502001143Search in Google Scholar

[16] MA, Q.-H.-PEČARIČ, J.-ZHANG, J.-M.: Integral inequalities of systems and the estimatefor solutions of certain nonlinear two-dimensional fractional differential systems, Comput. Math. Appl. 61 (2011), 3258-3267.10.1016/j.camwa.2011.04.008Search in Google Scholar

[17] MEDVEĎ, M.: A new approach to an analysis of Henry type integral inequalities andtheir Bihari type versions, J. Math. Anal. Appl. 214 (1997), 349-366.10.1006/jmaa.1997.5532Search in Google Scholar

[18] MEDVEĎ, M.: Integral inequalities and global solutions of semilinear evolution equations, J. Math. Anal. Appl. 37 (2002), 871-882.Search in Google Scholar

[19] MEDVEĎ, M.-MOUSSAOUI, T.: Asymptotic integration of nonlinear Φ-Laplacian differentialequations, Nonlinear Anal. 72 (2010), 1-8.10.1016/j.na.2009.09.042Search in Google Scholar

[20] MEDVEĎ, M.: On the asymptotic behavior of solutions of nonlinear differential equationsof integer and also of non-integer order, in: Proc. 9th Colloquium on the Qual. Theory of Differ. Equ., Szeged, Hungary, 2011, Electron. J. Qual. Theory Differ. Equ. 10 (2012), pp. 1-9.Search in Google Scholar

[21] MEDVEĎ, M.-PEKÁRKOVÁ, E.: Long time behavior of second order differential equationswith p-Laplacian, Electron. J. Qual. Theory Differ. Equ. 108 (2008), 1-12.Search in Google Scholar

[22] MILLER, K. S.-ROSS, B.: An Introduction to the Fractional Calculus and DifferentialEquations. John Wiley, New York, 1993.Search in Google Scholar

[23] MUSTAFA, O. G.-ROGOVCHENKO, Y. V.: Global existence of solutions with prescribedasymptotic behavior for second-order nonlinear differential equations, Nonlinear Anal. 51 (2002), 339-368.10.1016/S0362-546X(01)00834-3Search in Google Scholar

[24] PODLUBNY, I.: Fractional Differential Equations. Academic Press, San Diego, 1999.Search in Google Scholar

[25] PHILOS, CH. G.-PURNARAS I. K.-TSAMATOS, P. CH.: Large time asymptotic topolynomials solutions for nonlinear differential equations, Nonlinear Anal. 59 (2004), 1157-1179. 10.1016/j.na.2004.08.011Search in Google Scholar

[26] PRUDNIKOV, A. P.-BRYCHKOV, ZU. A.-MARICHEV, O. I.: Integral and Series, in: Elementary Functions, Vol. 1, Nauka, Moscow, 1981. (In Russian)Search in Google Scholar

[27] ROGOVCHENKO, Y. V.: On asymptotics behavior of solutions for a class of secondorder nonlinear differential equations, Collect. Math. 49 (1998), 113-120.Search in Google Scholar

[28] ROGOVCHENKOS. P.-ROGOVCHENKO, YU. V.: Asymptotics of solutions for a classof second order nonlinear differential equations, Portugal. Math. 57 (2000), 17-32.Search in Google Scholar

[29] SAMKO, S. G.-KILBAS, A. A.-MARICHEV, O. I.: Fractional Integarals and Derivatives:Theory and Applications. Gordon and Breach Sci. Publ., New York, 1993.Search in Google Scholar

[30] TONG, J.: The asymptotic behavior of a class of nonlinear differential equations of secondorder, Proc. Amer. Math. Soc. 84 (1982), 235-236.10.1090/S0002-9939-1982-0637175-4Search in Google Scholar

[31] TRENCH, W. F.: On the asymptotic behavior of solutions of second order linear differentialequations, Proc. Amer. Math. Soc. 54 (1963), 12-14.10.1090/S0002-9939-1963-0142844-7Search in Google Scholar