Journal of Integral Equations and Applications

Nonlocal initial boundary value problem for a fractional integrodifferential equation in a Banach space

A. Anguraj and P. Karthikeyan

Full-text: Open access

Article information

Source
J. Integral Equations Applications, Volume 24, Number 2 (2012), 183-194.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1340369461

Digital Object Identifier
doi:10.1216/JIE-2012-24-2-183

Mathematical Reviews number (MathSciNet)
MR2945801

Zentralblatt MATH identifier
1253.34072

Subjects
Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

Keywords
Existence of solution fractional integro differential equation Krasnoselkii theorem contraction mapping principle

Citation

Anguraj, A.; Karthikeyan, P. Nonlocal initial boundary value problem for a fractional integrodifferential equation in a Banach space. J. Integral Equations Applications 24 (2012), no. 2, 183--194. doi:10.1216/JIE-2012-24-2-183. https://projecteuclid.org/euclid.jiea/1340369461


Export citation

References

  • B. Ahmad and J.J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. Value Prob. 2009 (2009), Article ID 708576.
  • A. Anguraj and P. Karthikeyan, Existence of solutions for fractional semilinear evolution boundary value problem, Commun. Appl. Anal. 14 (2010), 505-514.
  • A. Anguraj, P. Karthikeyan and G.M. N'Guérékata, Nonlocal Cauchy problem for some fractional abstract integrodifferential equations in Banach space, Commun. Math. Anal. 6 (2009), 1-6.
  • B. Bonilla, M. Rivero, L. Rodriguez-Germa and J.J. Trujillo, Fractional differential equations as alternative models to nonlinear differential equations, Appl. Math. Comput. 187 (2007), 79-88.
  • M. Caputo, Linear models of dissipation whose $q$ is almost frequently independent, Part II, J. Ray. Astr. Soc. 13 (1967), 529-539.
  • C. Cuevas and J. Cesar de Souza, Existence of $S$-asympototically $\omega$ periodic solutions for fractional order functional integrodifferential equations with infinite delay, Nonlinear Anal. 72 (2010), 1683-1689.
  • Zhenbin Fan and Gang Li, Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal. 258 (2010), 1709-1727.
  • O.K. Jaradat, A. Al-Omari and S. Momani, Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Anal. 69 (2008), 3153-3159.
  • A.A. Kilbas, Hari M. Srivastava and Juan J. Trujillo, Theory and applications of fractional differential equations, Vol. 204, North-Holland Math. Stud., Amsterdam, 2006.
  • V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, UK, 2009.
  • V. Lakshmikantham and A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (2008), 2977-2682.
  • Zhi-Wei Lv, Jin Liang and Ti-Jun Xiao, Solutions to fractional differential equations with nonlocal initial condition in Banach spaces, Adv. Difference. Equations 2010, Article ID 340349.
  • K.S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, Inc., New York, 1993.
  • G.M. Mophou, O. Nakoulima and G.M. N'Guérékata, Existence results for some fractional differential equations with nonlocal conditions, Nonlinear Stud. 17 (2010), 15-21.
  • G.M. N'Guérékata, A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear Anal. 70 (2009), 1873-1876.
  • –––, Existence and uniqueness of an integral solution to some Cauchy problem with nonlocal conditions, in: Differential and difference equations and applications, 843-849, Hindawi Public Corporation, New York, 2006.
  • I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
  • S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives: Theory and applications, Gordan and Breach, Amsterdam, 1993.
  • H.L. Tidke, Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions, Electron. J. Differential Equations 2009 (2009), 1-7.
  • Xingmei Xue, Nonlinear differential equations with nonlocal conditions in Banach spaces, Nonlinear Anal. 63 (2005), 575-586. \noindentstyle