Some basic results for fractional functional integro-differential equations

Communications in Applied Analysis

Volumn 12, Issue 4, 2008, Pages 467-478

  Bashir, Ahmad ^a   Sivasundaram, S ^a  

^a NONE

Author keywords

Extremal solutions; Fractional integro differential equations; Local and global existence

Indexed keywords

EID: 69549122072     PISSN: 10832564     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008) 1340-1350.
2. K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), 630-637.
3. K. Diethelm, A. D. Freed, On the solution of nonlinear fractional differential equations used in the modeling of viscoplasticity, in: F. Keil, W. Mackens, H. Vob, J. Werther (Eds.), Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, Springer, Heidelberg, 1999, pp. 217-224.
4. K. Diethelm, N. J. Ford, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comput. 154 (2004) 621-640.
5. V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (2008) 2677-2682.
6. V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal. 69 (2008) 3337-3343.
7. V. Lakshmikantham, A. S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Appl. Anal. 11(2007) 395-402.
8. V. Lakshmikantham, M.R.M. Rao, Theory of Integro-Differential Equations, Gordon & Breach, London, 1995.
9. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
10. G. M. N'Guerekata, A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear Anal. doi:10.1016/j.na.2008.02.087 (In Press).
11. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
12. S. G. Samko, A. A. Kilbas, I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.