Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 8 (2013), 115 -- 124

ON A FRACTIONAL DIFFERENTIAL INCLUSION WITH FOUR-POINT INTEGRAL BOUNDARY CONDITIONS

Aurelian Cernea

Abstract. We study the existence of solutions for fractional differential inclusions of order q∈ (1,2] with four-point integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps.

2010 Mathematics Subject Classification: 34A60; 34B10; 34B15.
Keywords: Fractional differential inclusion; Caputo fractional derivative; Boundary value problem; Integral boundary conditions.

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References

  1. B. Ahmad, S. K. Ntouyas, Boundary value problems for fractional differential inclusions with four-point integral boundary conditions, Surveys Math. Appl. 6 (2011), 175-193. MR2970722.

  2. E. Ait Dads, M. Benchohra, S. Hamani, Impulsive fractional differential inclusions involving Caputo fractional derivative, Fract. Calc. Appl. Anal. 12 (2009), 15-38. MR2494428(2009m:34018). Zbl 1179.26012.

  3. J. P. Aubin, A. Cellina, Differential Inclusions, Springer, Berlin, 1984. MR0755330(85j:49010). Zbl 0538.34007.

  4. C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions, Springer, Berlin, 1977. MR08467319(57 #7169). Zbl 0346.46638.

  5. A. Cernea, An existence result for a Fredholm-type integral inclusion, Fixed Point Theory 9 (2008), 441-447. MR2464124(2009i:34019). Zbl 1162.45003.

  6. A. Cernea, On the existence of solutions for fractional differential inclusions with boundary conditions, Fract. Calc. Appl. Anal. 12 (2009), 433-442. MR2598190(2010m:34018). Zbl 1206.34011.

  7. A. Cernea, A note on the existence of solutions for some boundary value problems of fractional differential inclusions, Fract. Calc. Appl. Anal. 15 (2012), 183-194. MR2897772. Zbl 06194281.

  8. Y.K. Chang, J.J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions, Mathematical and Computer Modelling 49 (2009), 605-609. MR2483665(2009m:34020).

  9. H. Covitz, S.B. Nadler jr., Multivalued contraction mapping in generalized metric spaces, Israel J. Math. 8 (1970), 5-11. MR0263062(41 #7667). Zbl 0192.59802.

  10. A.F. Filippov, Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621. MR0220995(36 #4047). Zbl 0238.34010.

  11. Z. Kannai, P. Tallos, Stability of solution sets of differential inclusions, Acta Sci. Math. (Szeged) 61 (1995), 197-207. MR1377359(96m:34027). Zbl 0851.34015.

  12. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. MR2218073(2007a:34002). Zbl 1092.45003.

  13. T.C. Lim, On fixed point stability for set-valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985), 436-441. MR0805266(86m:47086). Zbl 0593.47056.

  14. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. MR1658022(99m:26009). Zbl 0924.34008.

  15. P. Tallos, A Filippov-Gronwall type inequality in infinite dimensional space, Pure Math. Appl. 5 (1994), 355-362. MR1343457(96e:34033). Zbl 0827.34008.



Aurelian Cernea
Faculty of Mathematics and Computer Science,
University of Bucharest,
Academiei 14, 010014 Bucharest, Romania.
e-mail: acernea@fmi.unibuc.ro




http://www.utgjiu.ro/math/sma