Uneingeschränkter Zugang

Existence of three positive solutions for boundary value problem with fractional order and infinite delay

   | 12. Dez. 2015

Zitieren

[1] Ravi P. Agarwal, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations., Journal of Mathem. Anal. and Applications, 371, (2010), 57-58.10.1016/j.jmaa.2010.04.034Search in Google Scholar

[2] Ravi P. Agarwal, Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half line., Dynamics of Continuous Discrete and Impulsive System, 18, (2011), 235-244.Search in Google Scholar

[3] Zhanbig Bainov, Positive solutions for boundary value problem of nonlinear frac- tional differential equation, Journal of Mathematical Anal and Application, 311, (2005), 495-505.10.1016/j.jmaa.2005.02.052Search in Google Scholar

[4] Ahmad Bachir, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations, Applied Mathematics Letters, 23, (2010), 390-394.10.1016/j.aml.2009.11.004Search in Google Scholar

[5] Ahmad Bachir, Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Boundary Value Problems, 36, (2011), 9 pp.10.1186/1687-2770-2011-36Search in Google Scholar

[6] Jorge Caballero, Positive solutions for a class of singular fractional boundary value problems., Computers Mathematics with Applications, 62, (2011), 1325-1332.10.1016/j.camwa.2011.04.013Search in Google Scholar

[7] Keller Diethelm, On the solution of nonlinear fractional order differential equa- tions used in the modeling of thermoplasticity, in "Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics,Reaction Engineering and Molecular Properties, Springer-Verlag, (1999), 217-224.10.1007/978-3-642-60185-9_24Search in Google Scholar

[8] Jiqin Deng, Existence and uniqueness of solutions of initial value problems for non- linear fractional differential equations, Applied Mathematics Letters, 23, (2010), 676-680.10.1016/j.aml.2010.02.007Search in Google Scholar

[9] Ahmad El Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Analysis, 33, (1998), 181-186.10.1016/S0362-546X(97)00525-7Search in Google Scholar

[10] El Sayed Ahmad, Multivalued fractional differential equations, Applied Mathemat- ical Computation, 68, (1995), 15-25.10.1016/0096-3003(94)00080-NSearch in Google Scholar

[11] Dagun Guo, Nonlinear Problems in Abstract Cones, Academic Press, Boston., 1988Search in Google Scholar

[12] Jack Hale, Phase space for retarded equations with infinite delay, Funkcialaj Ekva- cioj, 21, (1978), 11-41.Search in Google Scholar

[13] Yoshiyuki Hino, Functional Differential Equations with Infinite Delay, Springer- Verlag, Berlin, 1991.Search in Google Scholar

[14] Franz Kappel, Some considerations to the fundamental theory of infinite delay equations, Journal of Differential Equations, 37, (1980), 141-183.10.1016/0022-0396(80)90093-5Search in Google Scholar

[15] Ralph Koeller, Application of fractional calculus to the theory of viscolasticity, Journal of Applied Mechanics, 51, (1984), 299-307.10.1115/1.3167616Search in Google Scholar

[16] Nickolai Kosmatov, A singular boundary value problem for nonlinear differential equations of fractional order, Journal of Applied Mathematics and Computing, 28, (2009), 125-135.10.1007/s12190-008-0104-xSearch in Google Scholar

[17] Anatoly Kilbas, Theory and Applications of Fractional Differential Equations, El- sevier Science B.V., Amsterdam., 2006Search in Google Scholar

[18] vangipuram Lakshmikantham, Theory of Fractional Dynamic Systems, Cam- bridge Academic Publishers, Cambridge., 2009Search in Google Scholar

[19] Williams Legett, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana University Mathematics Journal, 428, (1979), 673-688.Search in Google Scholar

[20] Wei Lin, Global existence theory and chaos control of fractional differential equa- tions, Journal of Mathematical Analysis and Applications, 332, (2007), 709-726.10.1016/j.jmaa.2006.10.040Search in Google Scholar

[21] Li Congming, Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers Mathematics with Applications, 59, (2010), 1363-1375.10.1016/j.camwa.2009.06.029Search in Google Scholar

[22] Yang Liu, A sufficient condition for the existence of a positive solution for a non- linear fractional differential equation with the Riemann Liouville derivative, Applied Mathematics Letters, 25, (2012), 1986-1992.10.1016/j.aml.2012.03.018Search in Google Scholar

[23] Kenneth Miller, An Introduction to the Fractional Calculus and Fractional Differ- ential Equations, Wiley, New York., 1993Search in Google Scholar

[24] Zaid Odibat, An algorithm for the numerical solution of differential equations of fractional order, Journal of Applied Mathematics Informatics, 26, (2008), 15-27.Search in Google Scholar

[25] Igor Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional Calculus and Applied Analysis, 5, (2002), 367-386.Search in Google Scholar

[26] Tingting Qiu, Existence of positive solutions for singular fractional differential equa- tions, Electronic Journal of Differential Equations, (2008), 1-9.Search in Google Scholar

[27] Konrad Schumacher, Existence and continuous dependence for differential equa- tions with unbounded delay, Archive for Rational Mechanics and Analysis, 64, (1978), 315-335.10.1007/BF00247662Search in Google Scholar

[28] Shuqin Zhang, Positive solutions for boundary-value problems of nonlinear frac- tional differential equations, Electron. J. Differential Equations, 36, (2006), 1-12.10.1155/2007/76493Search in Google Scholar

[29] Yige Zhao, Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations, Applied Mathematics and Computation, (2011), 6950-6958. 10.1016/j.amc.2011.01.103Search in Google Scholar

eISSN:
1841-3307
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
Volume Open
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines