Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 14 (2019), 195 -- 202

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ON A BAGLEY-TORVIK FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSION

Aurelian Cernea

Abstract. Existence of solutions for a Bagley-Torvik fractional integro-differential inclusion is investigated in the case when the values of the set-valued map are not convex.

2010 Mathematics Subject Classification: 34A60; 34A08
Keywords: Fractional derivative; differential inclusion; boundary conditions

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References

  1. R.P. Agarwal, A.A. Saedi, N. Alghamdi, S.K. Ntouyas, B. Ahmad, Existence results for multi-term fractional differential equations with nonlocal multi-point and multi-strip boundary conditions, Adv. Difference. Eqs. 2018, no. 342 (2018), 1-23. MR3858463. Zbl 0700798.

  2. J.P. Aubin, H. Frankowska, Set-valued Analysis, Birkhauser, Basel, 1990. MR1048347. Zbl 1168.49014.

  3. D. Băleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific, Singapore, 2012. MR2894576. Zbl 1347.26006.

  4. A. Cernea, Filippov lemma for a class of Hadamard-type fractional differential inclusions, Fract. Calc. Appl. Anal. 18 (2015), 163-171. MR3316535. Zbl 1310.45008.

  5. A. Cernea, On the existence of solutions for a Hadamard-type fractional integro-differential inclusion, J. Nonlin. Anal. Optim. 6 (2015), 67-72. MR3600625. Zbl 06928045.

  6. A. Cernea, On some boundary value problems for a fractional integro-differential inclusion, Nonlin. Funct. Anal. Appl. 21 (2016) 215-223. Zbl 1366.45006.

  7. L. Chen, G. Li, Existence results for generalized Bagley-Torvik type fractional differential inclusions with nonlocal initial conditions, J. Funct. Spaces 2018, ID 2761321 (2018), 1-9.

  8. K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010. MR2680847.

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

  10. B.H. Ibrahim, Q. Dong, Z.Fan, Existence for boundary value problems of two-term Caputo fractional differential equations, J. Nonlin. Sci. Appl. 10 (2017), 511-520. MR3623016.

  11. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. MR2218073. Zbl 1092.45003.

  12. K. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. MR1219954. Zbl 0789.26002.

  13. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. MR1658022. Zbl 0924.34008.

  14. P.J. Torvik, R. L. Bagley, On the appearence of the fractional derivative in the behavior of real materials, J. Appl. Mech. 51 (1984), 294-298. Zbl 1203.74022.




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