International Journal of Differential Equations

Existence of Solutions for Fractional Impulsive Integrodifferential Equations in Banach Spaces

Haide Gou and Baolin Li

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Abstract

We investigate the existence of solutions for a class of impulsive fractional evolution equations with nonlocal conditions in Banach space by using some fixed point theorems combined with the technique of measure of noncompactness. Our results improve and generalize some known results corresponding to those obtained by others. Finally, two applications are given to illustrate that our results are valuable.

Article information

Source
Int. J. Differ. Equ., Volume 2016 (2016), Article ID 5648798, 11 pages.

Dates
Received: 14 September 2016
Accepted: 1 November 2016
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881461

Digital Object Identifier
doi:10.1155/2016/5648798

Mathematical Reviews number (MathSciNet)
MR3584218

Zentralblatt MATH identifier
1355.34115

Citation

Gou, Haide; Li, Baolin. Existence of Solutions for Fractional Impulsive Integrodifferential Equations in Banach Spaces. Int. J. Differ. Equ. 2016 (2016), Article ID 5648798, 11 pages. doi:10.1155/2016/5648798. https://projecteuclid.org/euclid.ijde/1484881461


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References

  • R. P. Agarwal, M. Benchohra, and S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 973–1033, 2010.MR2596185
  • M. Benchohra, J. R. Graef, and S. Hamani, “Existence results of nonlinear fractional differential equations on reflexive Banach spaces,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 54, pp. 1–10, 2010.
  • M. Benchohra, S. Hamani, and S. K. Ntouyas, “Boundary value problems for differential equations with fractional order and nonlocal conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2391–2396, 2009.MR2532767
  • X. B. Shu and Q. Q. Wang, “The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order $1<\alpha <2$,” Computers and Mathematics with Applications, vol. 64, pp. 2100–2110, 2012.
  • M. Benchohra, J. Henderson, and S. Ntouyas, “Impulsive differential equations and inclusions,” Contemporary Mathematics and its Applications, vol. 2, 2006.
  • V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, Singapore, 1989.MR1082551
  • Y. X. Li, “Existence of solutions to initial value problems for abstract semilinear evolution equations,” Acta Mathematica Sinica, vol. 48, no. 6, pp. 1089–1094, 2005.MR2205049
  • Z. M. He and X. M. He, “Monotone iterative technique for impulsive integro-differential equations with periodic boundary conditions,” Computers & Mathematics with Applications, vol. 48, no. 1-2, pp. 73–84, 2004.MR2086786
  • L. Byszewski, “Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem,” Journal of Mathematical Analysis and Applications, vol. 162, no. 2, pp. 494–505, 1991.MR1137634
  • G. M. N'Guérékata, “A Cauchy problem for some fractional abstract differential equation with non local conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 5, pp. 1873–1876, 2009.MR2492125
  • K. Balachandran and J. Y. Park, “Nonlocal Cauchy problem for abstract fractional semilinear evolution equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 10, pp. 4471–4475, 2009.MR2548677
  • K. Balachandran, S. Kiruthika, and J. J. Trujillo, “Existence results for fractional impulsive integrodifferential equations in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1970–1977, 2011.MR2736061
  • H. D. Gou and B. L. Li, “Local and global existence of mild solution to impulsive fractional semilinear integro-differential equation with noncompact semigroup,” Communications in Nonlinear Science and Numerical Simulation, vol. 42, pp. 204–214, 2017.MR3534932
  • Y. Zhou and F. Jiao, “Existence of mild solutions for fractional neutral evolution equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1063–1077, 2010.MR2579471
  • P. Chen and Y. Li, “Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal conditions,” Zeitschrift für Angewandte Mathematik und Physik, vol. 65, no. 4, pp. 711–728, 2014.
  • J. Banas and K. Goebel, Measure of Noncompactness in Banach Spaces, vol. 60 of Lecture Notes in Pure and Applied Mathematics, Marcel Pekker, New York, NY, USA, 1980.
  • M. M. El-Borai, “Some probability densities and fundamental solutions of fractional evolution equations,” Chaos, Solitons and Fractals, vol. 14, no. 3, pp. 433–440, 2002.MR1903295
  • H. Lakzian, D. Gopal, and W. Sintunavarat, “New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations,” Journal of Fixed Point Theory and Applications, vol. 18, no. 2, pp. 251–266, 2016.MR3506286
  • K. Deimling, Nonlinear Functional Analysis, Springer, New York, NY, USA, 1985.MR787404 \endinput