References
- A. Arara, M. Benchohra, N. Hamidi and J. Nieto, Fractional order differential equations on an unbounded domain, Nonlinear Analysis 72 (2010), 580-586. https://doi.org/10.1016/j.na.2009.06.106
- R. P. Agarwal, M. Benchohra and B. A. Slimani, Existence results for differential equations with fractional order and impulses, Mem. Differential Equations Math. Phys. 44 (2008), 1-21. https://doi.org/10.1134/S0012266108010011
- B. Ahmad and J. J. Nieto, Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory, Topological Methods in Nonlinear Analysis 35 (2010), 295-304.
- B. Ahmad and J. J. Nieto, Existence of solutions for impulsive anti-periodic boundary value problems of fractional order, Taiwanese Journal of Mathematics 15 (3) (2011), 981-993. https://doi.org/10.11650/twjm/1500406279
- B. Ahmad and S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems 3 (2009), 251-258. https://doi.org/10.1016/j.nahs.2009.01.008
- M. Benchohra, J. Graef and S. Hamani, Existence results for boundary value problems with nonlinear frational differential equations, Applicable Analysis 87 (2008), 851-863. https://doi.org/10.1080/00036810802307579
- M. Belmekki, Juan J. Nieto and Rosana Rodriguez-Lopez, Existence of periodic solution for a nonlinear fractional differential equation, Boundary Value Problems 2009 (2009), Article ID 324561, doi:10.1155/2009/324561.
- M. Belmekki, Juan J. Nieto and Rosana Rodriguez-Lopez, Existence of solution to a periodic boundary value problem for a nonlinear impulsive fractional differential equation, Electronic Journal of Qualitative Theory of Differential Equations 16 (2014), 1-27.
- M. Benchohra and B. A. Slimani, Impulsive fractional differential equations, Electron. J. Differential Equations 10 (2009), 1-11.
- R. Caponetto, G. Dongola and L. Fortuna, Frational order systems Modeling and control applications, World Scientific Series on nonlinear science, Ser. A, Vol. 72, World Scientific, Publishing Co. Pte. Ltd. Singapore, 2010.
- K. Diethelm, Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution, J. Eur. Syst. Autom. 42 (2008), 665-676.
- W. H. Deng and C. P. Li, Chaos synchronization of the fractional Lu system, Physica A 353 (2005), 61-72. https://doi.org/10.1016/j.physa.2005.01.021
- J. Dabas, A. Chauhan, and M. Kumar, Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay, International Journal of Differential Equations 2011 (2011), Article ID 793023, 20 pages.
- R. Dehghant and K. Ghanbari, Triple positive solutions for boundar, Bulletin of the Iranian Mathematical Society 33 (2007), 1-14.
- S. Das and P.K.Gupta, A mathematical model on fractional Lotka-Volterra equations, Journal of Theoretical Biology 277 (2011), 1-6. https://doi.org/10.1016/j.jtbi.2011.01.034
- H. Ergoren and A. Kilicman, Some Existence Results for Impulsive Nonlinear Fractional Differential Equations with Closed Boundary Conditions, Abstract and Applied Analysis 2012 (2012), Article ID 387629, 15 pages.
- M. Feckan, Y. Zhou and J. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commun Nonlinear Sci Numer Simulat 17 (2012), 3050-3060. https://doi.org/10.1016/j.cnsns.2011.11.017
- L. J. Guo, Chaotic dynamics and synchronization of fractional-order Genesio-Tesi systems, Chinese Physics 14 (2005), 1517-1521. https://doi.org/10.1088/1009-1963/14/8/007
-
G. L. Karakostas, Positive solutions for the
${\Phi}$ -Laplacian when${\Phi}$ is a sup-multiplicative-like function, Electron. J. Diff. Eqns. 68 (2004), 1-12. - E. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electronic Journal of Qualitative Theory of Differential Equations, 3 (2008), 1-11.
- A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Frational Differential Equations, Elsevier Science B. V. Amsterdam, 2006.
- Y. Liu, Positive solutions for singular FDES, U.P.B. Sci. Series A, 73 (2011), 89-100.
- Y. Liu, Solvability of multi-point boundary value problems for multiple term Riemann-Liouville fractional differential equations, Comput. Math. Appl. 64 (4) (2012), 413-431. https://doi.org/10.1016/j.camwa.2011.12.004
- C. Li and G. Chen, Chaos and hyperchaos in the fractional-order Rossler equations, Physica A 341 (2004), 55-61. https://doi.org/10.1016/j.physa.2004.04.113
- Z. Liu and X. Li, Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations, Communications in Nonlinear Science and Numerical Simulation, 18 (6) (2013), 1362-1373. https://doi.org/10.1016/j.cnsns.2012.10.010
- Z. Liu, L. Lu and I. Szanto, Existence of solutions for fractional impulsive differential equations with p-Laplacian operator, Acta Mathematica Hungarica 141 (3) (2013), 203-219. https://doi.org/10.1007/s10474-013-0305-0
- J. Mawhin, Topological degree methods in nonlinear boundary value problems, in: NSFCBMS Regional Conference Series in Math., American Math. Soc. Providence, RI, 1979.
- G. M. Mophou, Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal. 72 (2010), 1604-1615. https://doi.org/10.1016/j.na.2009.08.046
- K. S. Miller and S. G. Samko, Completely monotonic functions, Integr. Transf. Spec. Funct. 12 (2001), 389-402. https://doi.org/10.1080/10652460108819360
- A. M. Nakhushev, The Sturm-Liouville Problem for a Second Order Ordinary Differential equations with fractional derivatives in the lower terms, Dokl. Akad. Nauk SSSR 234 (1977), 308-311.
- J. J. Nieto, Maximum principles for fractional differential equations derived from Mittag-Leffler functions, Applied Mathematics Letters 23 (2010), 1248-1251. https://doi.org/10.1016/j.aml.2010.06.007
- J. J. Nieto, Comparison results for periodic boundary value problems of fractional differential equations, Fractional Differential Equations 1 (2011), 99-104.
- N Ozalp and I Koca, A fractional order nonlinear dynamical model of interpersonal relationships, Advances in Difference Equations, (2012) 2012, 189. https://doi.org/10.1186/1687-1847-2012-189
- I. Petras, Chaos in the fractional-order Volta's system: modeling and simulation, Nonlinear Dyn. 57 (2009), 157-170. https://doi.org/10.1007/s11071-008-9429-0
- I. Petras, Fractional-Order Feedback Control of a DC Motor, J. of Electrical Engineering 60 (2009), 117-128.
- I. Podlubny, Frational Differential Equations, Mathematics in Science and Engineering, Academic Press, San Diego, USA, 1999.
- S. Z. Rida, H.M. El-Sherbiny and A. Arafa, On the solution of the fractional nonlinear Schrodinger equation, Physics Letters A 372 (2008), 553-558. https://doi.org/10.1016/j.physleta.2007.06.071
- M. Rehman and R. Khan, A note on boundaryvalueproblems for a coupled system of fractional differential equations, Computers and Mathematics with Applications 61 (2011), 2630-2637. https://doi.org/10.1016/j.camwa.2011.03.009
- G. Wang, B. Ahmad and L. Zhang, Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Analysis 74 (2011), 792-804. https://doi.org/10.1016/j.na.2010.09.030
- X. Wang, C. Bai, Periodic boundary value problems for nonlinear impulsive fractional differential equations, Electronic Journal of Qualitative Theory and Differential Equations, 3 (2011), 1-15.
- X. Wang and H. Chen, Nonlocal Boundary Value Problem for Impulsive Differential Equations of Fractional Order, Advances in Difference Equations, (2011) 2011, 404917.
- Z. Wei, W. Dong and J. Che, Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative, Nonlinear Analysis: Theory, Methods and Applications 73 (2010), 3232-3238. https://doi.org/10.1016/j.na.2010.07.003
- Z. Wei and W. Dong, Periodic boundary value problems for Riemann-Liouville fractional differential equations, Electronic Journal of Qualitative Theory of Differential Equations, 87 (2011), 1-13.
- J. Wang, H. Xiang and Z. Liu, Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations, International Journal of Differential Equations 2010 (2010), Article ID 186928, 12 pages, doi:10.1155/2010/186928.
- P. K. Singh and T Som, Fractional Ecosystem Model and Its Solution by Homotopy Perturbation Method, International Journal of Ecosystem 2 (5) (2012), 140-149. https://doi.org/10.5923/j.ije.20120205.06
- Y. Tian and Z. Bai, Existence results for the three-point impulsive boundary value problem involving fractional differential equations, Computers and Mathematics with Applications 59 (2010), 2601-2609. https://doi.org/10.1016/j.camwa.2010.01.028
- M. S. Tavazoei and M. Haeri, Chaotic attractors in incommensurate fractional order systems, Physica D 327 (2008), 2628-2637.
- M. S. Tavazoei and M. Haeri, Limitations of frequency domain approximation for detecting chaos in fractional order systems, Nonlinear Analysis 69 (2008), 1299-1320. https://doi.org/10.1016/j.na.2007.06.030
- A. Yang and W. Ge, Positive solutions for boundary value problems of N-dimension nonlinear fractional differential systems, Boundary Value Problems, 2008, article ID 437453, doi: 10.1155/2008/437453.
- S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl. 252 (2000), 804-812. https://doi.org/10.1006/jmaa.2000.7123
- S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equation, Electron. J. Diff. Eqns. 36 (2006), 1-12.
- X. Zhao and W. Ge, Some results for fractional impulsive boundary value problems on infinite intervals, Applications of Mathematics 56 (4) (2011), 371-387. https://doi.org/10.1007/s10492-011-0021-4
- X. Zhang, X. Huang and Z. Liu, The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay, Nonlinear Analysis: Hybrid Systems 4 (2010), 775-781. https://doi.org/10.1016/j.nahs.2010.05.007
- Y. Zhao, S. Sun, Z. Han, M. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Applied Mathematics and Computation, 217 (2011), 6950-6958. https://doi.org/10.1016/j.amc.2011.01.103
- Z. Liu, L. Lu and I. Szanto, Existence of solutions for fractional impulsive differential equations with p-Laplacian operator, Acta Math. Hungar. 141 (2013), 203-219. https://doi.org/10.1007/s10474-013-0305-0
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