CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
Implementation of Feature Selection Using Correlation Matrix in Python

Ahmad Farhan AlShammari
Random Articles
Reseach Article

Existence Results for Fractional Order Mixed Type Functional Integro-differential Equations with Impulses

by R. Murugesu, S. Dhanalakshmi
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 73 - Number 17
Year of Publication: 2013
Authors: R. Murugesu, S. Dhanalakshmi
10.5120/12831-9985

R. Murugesu, S. Dhanalakshmi . Existence Results for Fractional Order Mixed Type Functional Integro-differential Equations with Impulses. International Journal of Computer Applications. 73, 17 ( July 2013), 5-10. DOI=10.5120/12831-9985

@article{ 10.5120/12831-9985,
author = { R. Murugesu, S. Dhanalakshmi },
title = { Existence Results for Fractional Order Mixed Type Functional Integro-differential Equations with Impulses },
journal = { International Journal of Computer Applications },
issue_date = { July 2013 },
volume = { 73 },
number = { 17 },
month = { July },
year = { 2013 },
issn = { 0975-8887 },
pages = { 5-10 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume73/number17/12831-9985/ },
doi = { 10.5120/12831-9985 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:40:20.442922+05:30
%A R. Murugesu
%A S. Dhanalakshmi
%T Existence Results for Fractional Order Mixed Type Functional Integro-differential Equations with Impulses
%J International Journal of Computer Applications
%@ 0975-8887
%V 73
%N 17
%P 5-10
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques.

References
  1. A. Anguraj and M. Mallika Arjunan, Existence and uniqueness of mild and classical solutions of impulsive evolution equations, Electron. J. Differ. Equ. 2005(2005), 111, 1-8.
  2. A. Anguraj, M. Mallika Arjunan and E. Hernandez, Existence results for impulsive neutral functional differential equations with state dependent delay, Appl. Anal. , 26(7)(2007), 861-872.
  3. K. Balachandran, S. Kiruthika and J. J. Trujillo, Existence results for fractional impulsive integrodifferential equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simul. , (2010).
  4. K. Balachandran, D. G. Park and S. M. Anthoni, Existence of solutions of abstract nonlinear second order neutral functional integrodifferential equations, Comput. Math. Appl. 46(2003), 1313.
  5. K. Balachandran, J. Y. Park and M. Chandrasekaran, Nonlocal Cauchy problem for delay integrodifferential equations of Sobolov type in Banach spaces, Appl. Math. Lett. 15(7)(2002), 845-854.
  6. E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph. D. Thesis, Eindhoven University of Technology, 2001.
  7. M. Benchora, J. Henderson and S. K. Ntouyas, Impulsive differential equations and inclusions, Hindawi publishing corporation, Newyork, 2006.
  8. M. Benchora, BA. Slimani, Existence and Uniqueness of solutions to impulsive fractional differential equations, Electron. J. Differ. Equ. , 2009(10), 1-11.
  9. Y. K. Chang, A. Anguraj and M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Anal. , Hybrid Syst. , 2(1)(2008), 209-218.
  10. Y. K. Chang, V. Kavitha and M. Mallika Arjunan, Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators, Nonlinear Anal. , Hybrid Syst. , 4(1)(2010), 32-43.
  11. J. Dabas, A. Chauhan and M. Kumar, Existence of the mild solutions for impulsive fractional equations with infinite delay, Int. J. Differ. Equations, 2011(2011).
  12. D. Delbosco, L. Rodino, Existence and uniqueness for a fractional differential equation, J. Math. Anal. Appl. , 204(1996), 609-625.
  13. M. B. Dhakne and S. D. Kender, On abstract Nonlinear Mixed Volterra-Fredholm Integrodifferential equations, Comm. Appl. Nonlinear Anal. , 13(4), (2006), 101-112.
  14. T. Diagana, G. M. Mophou and G. M. Guerekata, On the existence of mild solutions to some semilinear fractional integrodifferential equations, Electron. J. Qual. Theory Differ. Equ. , 58(2010), 1-17.
  15. A. Granas, J. Dugundji, Fixed Point Theory, Springer- Verlag, New York, 2003.
  16. Heping Jiang, Existence results for fractional order functional differential equations with impulse, Comput. Math. Appl. , 64(2012), 3477-3483.
  17. JinRong Wang, Michal Feckan, Yong Zhou. On the new concept of solutions and existence results for impulsive fractional evolution equations, Dyn. Partial Differ. Equ. , 8(2011), 345-361.
  18. JinRong Wang, Yong Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal. , RWA 12(2011), 262-272.
  19. JinRong Wang, Yong Zhou, Analysis of nonlinear fractional control systems in Banach spaces, Nonlinear Anal. , TMA 74(2011), 5929-5942.
  20. V. Kavitha, M. Mallika Arjunan and C. Ravichandran, Existence results for impulsive systems with nonlocal conditions in Banach Spaces, J. Nonlinear Sci. Appl. 4(2)(2011), 138-151.
  21. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, [in:]North Holland Math. stud. , vol. 204, Elsevier Science, 2006.
  22. V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal. 69(2008), 3337-3343.
  23. V. Lakshmikantham, A. S. Vastala, Basic theory of fractional differential equations, Nonlinear Anal. 69(2008), 2677-2682
  24. V. Lakshmikantham, J. Vasundhara Devi, Theory of fractional differential equations in Banach Spaces, Eur. J. Pure Appl. Math. , 1(2008), 38-45.
  25. K. S. Miller, B. Ross, An introduction to the Fractional Calculus and Differential equations, JohnWiley, New York, 1993.
  26. G. M. Mophou, G. M. N'Gurerekata, Existence of mild solution for some fractional differential equations with nonlocal conditions, Semigroup Forum, 79(2009), 315-322.
  27. G. M. Mophou, Existence and Uniqueness of mild solutions of mild solution to impulsive fractional differential equations, Nonlinear Anal. , 72(2010), 1604- 1615.
  28. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  29. H. L. Tidke and M. B. Dhakne, Existence of solutions for nonlinear mixed type integrodifferential equation of second order, Surv. Math. Appl. 5(2010), 61-72.
  30. J. Wang and W. Wei, A class of nonlocal impulsive problems for integrodifferential equations in Banach spaces, Results Math. , 58(2010), 379-397.
  31. Xiao-Bao Shu, Yongzeng Lai, Yuming Chen, The existence of mild solutions for impulsive fractional partial differential equations, Nonlinear Anal. , TMA (74)(2011), 2003-2011.
  32. Yong Zhou, Existence and Uniqueness of fractional functional differential equations with unbounded delay, Int. J. Dyn. Syst. Differ. Equ. , 1(2008), 239-244.
  33. Yong Zhou, Feng Jiao, Jing Li, Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear Anal. , TMA 71(2009), 3249- 3256.
Index Terms

Computer Science
Information Sciences

Keywords

Impulsive conditions Fractional differential equations Fixed point theorems

Powered by PhDFocusTM