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Local and extremal solutions of some fractional integrodifferential equation with impulses

Year 2013, Volume: 62 Issue: 1, 101 - 113, 01.02.2013
https://doi.org/10.1501/Commua1_0000000689

Abstract

References

  • K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence results for fractional impulsive in- tegrodiğ erential equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011) 1970–1977.
  • M. Benchohra, J. Henderson, S. Ntouyas, Impulsive Diğ erential Equations and Inclusions, Hindawi Publishing Corporation, New York, 2006.
  • M. Benchohra, B. A. Slimani, Existence and uniqueness of solutions to impulsive fractional diğ erential equations, Electronic Journal of Diğerential Equations, 2009 (2009), No. 10, pp. 1–11.
  • M. Feckan, Y. Zhou, J. Wang, On the Concept and Existence of Solution for Impulsive Fractional Diğ erential Equations, Commun. Nonlinear Sci. Numer. Simulat. (2011), doi: 10.1016/j.cnsns.2011.11.017.
  • G. Wanga, B. Ahmad, L. Zhanga, Some existence results for impulsive nonlinear fractional diğ erential equations with mixed boundary conditions, Comput. Math. Appl. 62 (2011) 1389– 1397.
  • A.A. Kilbas, H M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Diğ eren- tial Equations, North-Holland Mathematics Studies, 204 Elsevier Science B.V., Amsterdam, 2006.
  • V. Lakshmikantam, D. Bainov, P.S. Simeonov, Theory of Impulsive Diğ erential Equations, World Scienti…c, Singapore, 1989.
  • V. Lakshmikantam, A.S. Vatsala, Basic theory of fractional diğ erential equations, Nonlinear Anal. 69 (2008) 2677-2682.
  • K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Diğ erential Equations, John Wiley and Sons, 1993.
  • K.B. Oldham, J. Spanier, Fractional Calculus: Theory and Applications, Diğ erentiation and Integration to Arbitrary Order, Academic Press, New York, 1974.
  • X. Wang, Impulsive boundary value problem for nonlinear diğ erential equations of fractional order, Comput. Math. Appl. 62 (2011) 2383–2391.
  • Current address : LMA, Department of Mathematics, University of Badji-Mokhtar, Annaba

LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES

Year 2013, Volume: 62 Issue: 1, 101 - 113, 01.02.2013
https://doi.org/10.1501/Commua1_0000000689

Abstract

The subject of this work is to prove existence, uniqueness, and continuous dependence upon the data of solution to integrodifferential hyperbolic
equation with integral conditions. The proofs are based on a priori estimates
and Laplace transform method. Finally, the solution by using a numerical
technique for inverting the Laplace transforms is obtained.

References

  • K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence results for fractional impulsive in- tegrodiğ erential equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011) 1970–1977.
  • M. Benchohra, J. Henderson, S. Ntouyas, Impulsive Diğ erential Equations and Inclusions, Hindawi Publishing Corporation, New York, 2006.
  • M. Benchohra, B. A. Slimani, Existence and uniqueness of solutions to impulsive fractional diğ erential equations, Electronic Journal of Diğerential Equations, 2009 (2009), No. 10, pp. 1–11.
  • M. Feckan, Y. Zhou, J. Wang, On the Concept and Existence of Solution for Impulsive Fractional Diğ erential Equations, Commun. Nonlinear Sci. Numer. Simulat. (2011), doi: 10.1016/j.cnsns.2011.11.017.
  • G. Wanga, B. Ahmad, L. Zhanga, Some existence results for impulsive nonlinear fractional diğ erential equations with mixed boundary conditions, Comput. Math. Appl. 62 (2011) 1389– 1397.
  • A.A. Kilbas, H M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Diğ eren- tial Equations, North-Holland Mathematics Studies, 204 Elsevier Science B.V., Amsterdam, 2006.
  • V. Lakshmikantam, D. Bainov, P.S. Simeonov, Theory of Impulsive Diğ erential Equations, World Scienti…c, Singapore, 1989.
  • V. Lakshmikantam, A.S. Vatsala, Basic theory of fractional diğ erential equations, Nonlinear Anal. 69 (2008) 2677-2682.
  • K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Diğ erential Equations, John Wiley and Sons, 1993.
  • K.B. Oldham, J. Spanier, Fractional Calculus: Theory and Applications, Diğ erentiation and Integration to Arbitrary Order, Academic Press, New York, 1974.
  • X. Wang, Impulsive boundary value problem for nonlinear diğ erential equations of fractional order, Comput. Math. Appl. 62 (2011) 2383–2391.
  • Current address : LMA, Department of Mathematics, University of Badji-Mokhtar, Annaba
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Atmania Rahima This is me

Publication Date February 1, 2013
Published in Issue Year 2013 Volume: 62 Issue: 1

Cite

APA Rahima, A. (2013). LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 62(1), 101-113. https://doi.org/10.1501/Commua1_0000000689
AMA Rahima A. LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2013;62(1):101-113. doi:10.1501/Commua1_0000000689
Chicago Rahima, Atmania. “LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62, no. 1 (February 2013): 101-13. https://doi.org/10.1501/Commua1_0000000689.
EndNote Rahima A (February 1, 2013) LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62 1 101–113.
IEEE A. Rahima, “LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 62, no. 1, pp. 101–113, 2013, doi: 10.1501/Commua1_0000000689.
ISNAD Rahima, Atmania. “LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62/1 (February 2013), 101-113. https://doi.org/10.1501/Commua1_0000000689.
JAMA Rahima A. LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62:101–113.
MLA Rahima, Atmania. “LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 62, no. 1, 2013, pp. 101-13, doi:10.1501/Commua1_0000000689.
Vancouver Rahima A. LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62(1):101-13.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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