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A note on fractional differential equations with fractional separated boundary conditions. (English) Zbl 1244.34004
Summary: We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.

34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
[1] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. · Zbl 1056.93542 · doi:10.1109/9.739144
[2] G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2008. · Zbl 1221.70024 · doi:10.1016/j.cnsns.2007.05.017
[3] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006. · Zbl 1206.26007 · doi:10.1016/S0304-0208(06)80001-0
[4] R. L. Magin, Fractional Calculus in Bioengineering, Begell House Publisher, West Redding, Conn, USA, 2006.
[5] J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007. · Zbl 1126.93335 · doi:10.1007/978-1-4020-6042-7_34
[6] R. P. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Advances in Difference Equations, Article ID 981728, p. 47, 2009. · Zbl 1182.34103 · doi:10.1155/2009/981728 · eudml:45519
[7] B. Ahmad and S. Sivasundaram, “Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions,” Communications in Applied Analysis, vol. 13, no. 1, pp. 121-127, 2009. · Zbl 1180.34003
[8] B. Ahmad and J. J. Nieto, “Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1838-1843, 2009. · Zbl 1205.34003 · doi:10.1016/j.camwa.2009.07.091
[9] B. Ahmad, “Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 4, pp. 390-394, 2010. · Zbl 1198.34007 · doi:10.1016/j.aml.2009.11.004
[10] 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, vol. 35, no. 2, pp. 295-304, 2010. · Zbl 1245.34008
[11] D. Baleanu, O. G. Mustafa, and R. P. Agarwal, “An existence result for a superlinear fractional differential equation,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1129-1132, 2010. · Zbl 1200.34004 · doi:10.1016/j.aml.2010.04.049
[12] E. Hernandez, D. O’Regan, and K. Balachandran, “On recent developments in the theory of abstract differential equations with fractional derivatives,” Nonlinear Analysis, vol. 73, no. 10, pp. 3462-3471, 2010. · Zbl 1229.34004 · doi:10.1016/j.na.2010.07.035
[13] B. Ahmad and S. Sivasundaram, “On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 480-487, 2010. · Zbl 1207.45014 · doi:10.1016/j.amc.2010.05.080
[14] B. Ahmad, S. K. Ntouyas, and A. Alsaedi, “New existence results for nonlinear fractional differential equations with three-point integral boundary conditions,” Advances in Difference Equations, Article ID 107384, p. 11, 2011. · Zbl 1204.34005 · doi:10.1155/2011/107384 · eudml:227693
[15] B. Ahmad and S. K. Ntouyas, “A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order,” Electronic Journal of Qualitative Theory of Differential Equations, no. 22, p. 15, 2011. · Zbl 1241.26004
[16] B. Ahmad and R. P. Agarwal, “On nonlocal fractional boundary value problems,” Dynamics of Continuous, Discrete & Impulsive Systems Series A, vol. 18, no. 4, pp. 535-544, 2011. · Zbl 1230.26003 · http://online.watsci.org/abstract_pdf/2011v18/v18n4a-pdf/9.pdf
[17] M. A. Krasnoselskii, “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, pp. 123-127, 1955.
[18] A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2005. · Zbl 1025.47002