Nonlocal controllability of mixed volterra-fredholm type fractional semilinear integro-differential inclusions in banach spaces

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 20, Issue 4, 2013, Pages 485-502

  Vijayakumar, V ^a   Ravichandran, C ^b   Murugesu, R ^c  

^a INFO INSTITUTE OF ENGINEERING   (India)

^b RVS College of Engineering and Technology   (India)

^c SRMV College of Arts and Science   (India)

Author keywords

Bohnenblust Karlin's fixed point theorem; Controllability; Integro differential equations; Mixed Volterra Fredholm type fractional differential inclusions; Nonlocal conditions

Indexed keywords

EID: 84884217875     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. N. Abada, M. Benchohra and H. Hammouche, Existence and controllability results for non-densely defined impulsive semilinear functional differential inclusions, J. Diff. Equ. 246 (2009), 3834-3863.
2. R.P. Agarwal, M. Benchohra and S. Hammani, A survey on existence results of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109(3) (2010), 973-1033.
3. R.P. Agarwal, V. Lakshmikantham and J.J. Nieto, On the concept of solution for fractional differential equations with uncertainly, Nonlinear Anal. 72(6) (2010), 2859-2862.
4. K. Balachandran and J.Y. Park, Controllability of fractional integro-differential systems in Banach spaces, Nonlinear Anal. 3 (2009) 363-367.
5. M. Benchohra and S.K. Ntouyas, Controllability for functional differential and integro-differential inclusions, J. Optim. Theory Appl. 113 (2002) 449-472. (Pubitemid 39583340)
6. M. Benchohra, E.P. Gatsori and S.K. Ntouyas, Controllability results for semilinear evolution inclusions with nonlocal conditions, J. Optim. Theory Appl. 118 (2003), 493-513.
7. M. Benchohra and A. Ouahab, Controllability results for functional semilinear differential inclusions in Frechet spaces, Nonlinear Anal. 61 (2005), 405-423. (Pubitemid 40274753)
8. H.F. Bohnenblust and S. Karlin, On a Theorem of Ville, in: Contributions to the Theory of Games, vol. I, Princeton University Press, Princeton, NJ, 1950, pp. 155-160.
9. L. Byszewski, Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
10. L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991), 11-19.
11. Y.K. Chang, A. Anguraj and M. Mallika Arjunan, Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces, Chaos Solitons & Fractals, 39(4) (2009), 1864-1876.
12. Y.K. Chang and D.N. Chalishajar, Controllability of mixed Volterra-Fredholm type integro-differential inclusions in Banach spaces, J. Franklin Inst. 345 (2008), 499-507.
13. J.P.C. dos Santos, V. Vijayakumar and R. Murugesu, Existence of mild solutions for nonlocal cauchy problem for fractional neutral integro-differential equation with unbounded delay, Commun. Math. Anal. 14(1) (2013), 59-71.
14. K. Deimling, Multivalued Differential Equations, De Gruyter, Berlin, 1992.
15. E. Hernandez and Donal O'Regan, Controllability of Volterra Fredholm type systems in Banach spaces, J. Franklin Inst. 346 (2009), 95-101.
16. S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis (Theory), Kluwer Academic Publishers, Dordrecht Boston, London, 1997.
17. B. Liu, Controllability of impulsive neutral functional differential inclusions with infinite delay, Nonlinear Anal. 60 (2005), 1533-1552. (Pubitemid 40206409)
18. B. Liu, Controllability of neutral functional differential and integro-differential inclusions with infinite delay, J. Optim. Theo. Appl. 123 (2004), 573-593. (Pubitemid 39499324)
19. B. Radhakrishnan and K. Balachandran, Controllability of impulsive neutral functional evolution integro-differential systems with infinite delay, Nonlinear Anal. Hybrid Syst. 5(4) (2011), 655-670.
20. C. Ravichandran and D. Baleanu, Existence results for fractional neutral functional integro-differential evolution equations with infinite delay in Banach spaces, Adv. Difference Equ., 215(2013), 1-12.
21. J.A. Machado, C. Ravichandran, M. Rivero and J.J. Trujillo, Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions, Fixed Point Theo. Appl. 66 (2013), 1-16.
22. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
23. 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.
24. V. Lakshmikantham, Theory of fractional differential equations, Nonlinear Anal. 60(10) (2008), 3337-3343.
25. V. Lakshmikantham and J.V. Devi, Theory of fractional differential equations in Banach spaces, Eur. J. Pure Appl. Math. 1 (2008), 38-45.
26. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V, Amsterdam, 2006.
27. A. Lasota and Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations or noncompact acyclic-valued map, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
28. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
29. M. Muslim, Existence and approximation of solutions to fractional differential equations, Math. Comput. Model. 49 (2009), 1164-1172.
30. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
31. V. Vijayakumar, C. Ravichandran and R. Murugesu, Approximate controllability for a class of fractional neutral integro-differential inclusions with state-dependent delay, Nonlinear stud. 20(4) (2013), 1-20.
32. J. Wang and Y. Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal. RWA, 12 (2011), 262-272.
33. J. Wang and Y. Zhou, Existence and controllability results for fractional semilinear differential inclusions, Nonlinear Anal. RWA, 12 (2011), 3642-3653.
34. J. Wang, Z. Fan and Y. Zhou, Nonlocal controllability of semilinear dynamic systems with fractional derivative in Banach spaces, J. Optim. Theo. Appl. DOI 10.1007/s10957-012-9999-3.
35. Y. Zhou and F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal. 11 (2010), 4465-4475.
36. Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010), 1063-1077.