Global attractivity for fractional order delay partial integro-differential equations

Advances in Difference Equations

Volumn 2012, Issue , 2012, Pages

  Abbas, Saïd ^a   Baleanu, Dumitru ^b,c   Benchohra, Mouffak ^d  

^a UNIVERSITY OF SAIDA   (Algeria)

^b CANKAYA UNIVERSITY   (Turkey)

^c INSTITUTE OF SPACE SCIENCES   (Romania)

^d UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Attractivity; Caputo fractional order derivative; Delay integro differential equation; Fixed point; Left sided mixed Riemann Liouville integral of fractional order; Solution

Indexed keywords

EID: 84867558935     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2012-62     Document Type: Article

References (17)

1. Kilbas, AA, Srivastava, HM, Trujillo, JJ: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies. Elsevier Science B.V, Amsterdam204 (2006)
2. Hilfer, R: Applications of Fractional Calculus in Physics. World Scientific, New Jersey (2000)
3. Baleanu, D, Diethelm, K, Scalas, E, Trujillo, JJ: Fractional Calculus Models and Numerical Methods. World Scientific Publishing, New York (2012)
4. Lakshmikantham, V, Leela, S, Vasundhara, J: Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009)
5. Podlubny, I: Fractional Differential Equations. Academic Press, San Diego (1999)
6. Abbas, S, Benchohra, M: Darboux problem for perturbed partial differential equations of fractional order with finite delay. Nonlinear Anal Hybrid Syst. 3, 597-604 (2009). doi:10.1016/j.nahs.2009.05.001
7. Abbas, S, Benchohra, M: Darboux problem for implicit impulsive partial hyperbolic differential equations. Electron J Diff Equ. 2011, 15 (2011)
8. Abbas, S, Benchohra, M, Vityuk, AN: On fractional order derivatives and Darboux problem for implicit differential equations. Fract Calc Appl Anal. 15, 168-182 (2012)
9. Vityuk, AN, Golushkov, AV: Existence of solutions of systems of partial differential equations of fractional order. Nonlinear Oscil. 7, 318-325 (2004). doi:10.1007/s11072-005-0015-9
10. Banaś, J, Dhage, BC: Global asymptotic stability of solutions of a functional integral equation. Nonlinear Anal Theory Methods Appl. 69, 1945-1952 (2008). doi:10.1016/j.na.2007.07.038
11. Banaś, J, Zaja̧c, T: A new approach to the theory of functional integral equations of fractional order. J Math Anal Appl. 375, 375-387 (2011). doi:10.1016/j.jmaa.2010.09.004
12. Darwish, MA, Henderson, J, O"Regan, D: Existence and asymptotic stability of solutions of a perturbed fractional functional integral equations with linear modification of the argument. Bull Korean Math Soc. 48, 539-553 (2011). doi:10.4134/BKMS.2011.48.3.539
13. Dhage, BC: Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem. Nonlinear Anal. 70, 2485-2493 (2009). doi:10.1016/j.na.2008.03.033
14. Dhage, BC: Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness. Diff Equ Appl. 2, 299-318 (2010)
15. Samko, SG, Kilbas, AA, Marichev, OI: Fractional Integrals and Derivatives. Theory Appl Gordon Breach Yverdon. (1993)
16. Corduneanu, C: Integral Equations and Stability of Feedback Systems. Acedemic Press, New York (1973)
17. Granas, A, Dugundji, J: Fixed Point Theory. Springer-Verlag New York (2003)