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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 4
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Articles

Boundary value problems for semilinear differential inclusions of fractional order in a Banach space

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Pages 571-591 | Received 02 Oct 2016, Accepted 20 Dec 2016, Published online: 23 Jan 2017

References

  • Abbas S, Benchohra M, N’Guerekata GM. Topics in fractional differential equations. Developments in mathematics. New York (NY): Springer; 2012.
  • Baleanu D, Diethelm K, Scalas E, et al. Fractional calculus models and numerical methods. New York (NY): World Scientific Publishing; 2012.
  • Bandyopadhyay B, Kamal S. Stabilization and control of fractional order systems: a sliding mode approach. New York (NY): Springer; 2015.
  • Diethelm K. The analysis of fractional differential equations. Berlin: Springer-Verlag; 2010.
  • Hilfer R. Applications of fractional calculus in physics. Singapore: World Scientific; 2000.
  • Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations, North-Holland mathematics studies. Vol. 204. Amsterdam: Elsevier Science B.V; 2006.
  • Miller KS, Ross B. An Introduction to the fractional calculus and fractional differential equations. New York (NY): Wiley; 1993.
  • Podlubny I. Fractional differential equations. San Diego: Academic Press; 1999.
  • Samko SG, Kilbas AA, Marichev OI. Fractional integrals and derivatives, theory and applications. Yverdon: Gordon and Breach Science Publishers; 1993.
  • Tarasov VE. Fractional dynamics. Applications of fractional calculus to dynamics of particles. Nonlinear physical science. Heidelberg: Springer, Beijing: Higher Education Press; 2010.
  • Anh CT, Ke TD. On nonlocal problems for retarded fractional differential equations in Banach spaces. Fixed Point Theory. 2014;15(2):373–392.
  • Ke TD, Loi NV, Obukhovskii V. Decay solutions for a class of fractional differential variational inequalities. Fract Calc Appl Anal. 2015;18(3):531–553.
  • Lakshmikantham V. Theory of fractional functional differential equations. Nonlinear Anal. 2008;69(10):3337–3343.
  • Lakshmikantham V, Vatsala AS. Basic theory of fractional differential equations. Nonlinear Anal. 2008;69(8):2677–2682.
  • Obukhovskii V, Yao J-C. Some existence results for fractional functional differential equations. Fixed Point Theory. 2010;11(1):85–96.
  • Wang R-N, Chen D-H, Xiao T-J. Abstract fractional Cauchy problems with almost sectorial operators. J. Differ Equ. 2012;252(1):202–235.
  • Zhang Z, Liu B. Existence of mild solutions for fractional evolution equations. Fixed Point Theory. 2014;15(1):325–334.
  • Zhou Y, Jiao F. Existence of mild solutions for fractional neutral evolution equations. Comput Math Appl. 2010;59(3):1063–1077.
  • Abbas S, Benchohra M, Darwish MA. New stability results for partial fractional differential inclusions with not instantaneous impulses. Fract Calc Appl Anal. 2015;18(1):172–191.
  • Benedetti I, Obukhovskii V, Taddei V. On noncompact fractional order differential inclusions with generalized boundary condition and impulses in a Banach space. J Funct Spaces. 2015; Article ID 651359, 10p.
  • Wang JR, Ibrahim AG, Fečkan M. Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces. Appl Math Comput. 2015;257:103–118.
  • Yan Z, Lu F. On approximate controllability of fractional stochastic neutral integro-differential inclusions with infinite delay. Appl Anal. 2015;94(6):1235–1258.
  • Wang JR, Ibrahim AG, Fečkan M. Differential inclusions of arbitrary fractional order with anti-periodic conditions in Banach spaces. Electron J Qual Theory Differ Equ. 2016; Paper No. 34, 22p.
  • Kamenskii M, Obukhovskii V, Zecca P. Condensing multivalued maps and semilinear differential inclusions in Banach spaces, de Gruyter series in Nonlinear analysis and applications. Vol. 7. Berlin: Walter de Gruyter; 2001.
  • Kamenskii M, Obukhovskii V, Petrosyan G. On semilinear fractional order differential inclusions in Banach spaces. Fixed Point Theory. 2017;18(1).
  • Ke TD, Obukhovskii V, Wong N-C, et al. On a class of fractional order differential inclusions with infinite delays. Appl Anal. 2013;92(1):115–137.
  • Deimling K. Multivalued differential equations, de Gruyter series in Nonlinear analysis and applications. Vol. 1. Berlin: Walter de Gruyter; 1992.
  • Ahmerov RR, Kamenskii MI, Potapov AS, et al. Measures of non-compactness and condensing operators. Boston: Birkhüser; 1992.
  • Borisovich YuG, Gelman BD, Myshkis AD. Introduction to the theory of multi-valued maps and differential inclusions. 2nd ed. Moscow: Publishing House ‘Librokom’; 2011. Russian.
  • Hyman DH. On decreasing sequences of compact absolute retracts. Fund Math. 1969;64:91–97.
  • Górniewicz L. Topological fixed point theory of multivalued mappings. 2nd ed. Topological fixed point theory and its applications. Vol. 4. Dordrecht: Springer; 2006.
  • Ekeland I, Temam R. Convex analysis and variational problems. Amsterdam: North Holland; 1976.

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