African Diaspora Journal of Mathematics
- Afr. Diaspora J. Math. (N.S.)
- Volume 12, Number 2 (2011), 13-25.
Fractional Integro-differential Equations with State-Dependent Delay on an Unbounded Domain
Full-text: Open access
Abstract
We are concerned with the existence of solutions for fractional integro-differential equations with state-dependent delay on an infinite interval. Our results are based on Schauder's fixed point theorem combined with the diagonalization process.
Article information
Source
Afr. Diaspora J. Math. (N.S.) Volume 12, Number 2 (2011), 13-25.
Dates
First available in Project Euclid: 13 October 2011
Permanent link to this document
https://projecteuclid.org/euclid.adjm/1318535325
Mathematical Reviews number (MathSciNet)
MR2847301
Zentralblatt MATH identifier
1244.34098
Keywords
Pseudo almost automorphic solutions Integro-differential equation integral resolvent family mild solution fixed point Diagonalization process
Citation
Benchohra, M.; Litimein , S. Fractional Integro-differential Equations with State-Dependent Delay on an Unbounded Domain. Afr. Diaspora J. Math. (N.S.) 12 (2011), no. 2, 13--25.https://projecteuclid.org/euclid.adjm/1318535325
References
- R.P. Agarwal, M. Benchohra, S. Hamani, S. Pinelas, Boundary value problem for differential equations involving Riemann-Liouville fractional derivative on the half line, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 18 (2011), 235-244. Mathematical Reviews (MathSciNet): MR2768132
- R.P. Agarwal and D. O'Regan, Infinite Interval Problems for Difference and Integral Equations, Kluwer Academic Publisher Dordrecht, 2001.
- A. Arara, M. Benchohra, N. Hamidi and J.J. Nieto, Fractional order differential equations on an unbounded domain. Nonlinear Anal. 72 (2010), 580-586. Mathematical Reviews (MathSciNet): MR2579326
- W. Arendt, C. Batty, M., Hieber, and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, 96 Birkhauser, Basel, 2001. Mathematical Reviews (MathSciNet): MR1886588
- S. Baghli and M. Benchohra, Uniqueness results for partial functional differential equations in Fréchet spaces, Fixed Point Theory 9 (2) (2008), 395-406. Mathematical Reviews (MathSciNet): MR2464126
- S. Baghli and M. Benchohra, Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces, Georgian Math. J. 17 (3) (2010), 423-436. Mathematical Reviews (MathSciNet): MR2719627
- S. Baghli and M. Benchohra, Global uniqueness results for partial functional and neutral functional evolution equations with infinite delay, Differential Integral Equations, 23 (1&2) (2010), 31-50.
- S. Baghli, M. Benchohra and G. N'Guérékata, Global results for functional evolution inclusions with state-dependent delay, J. Nonlinear Evo. Equ. Appl. (to appear).
- V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leiden, 1976.
- M. Benchohra and S. Litimein, A global uniqueness result for abstract integral equations of Volterra type in Banach spaces, Commun. Appl. Nonlinear Anal. 18 (2011), 37-44.
- C. Corduneanu and V. Lakshmikantham, Equations with unbounded delay: a survey. Nonlinear Anal. 4 (1980), 831-877. Mathematical Reviews (MathSciNet): MR586852
Zentralblatt MATH: 0449.34048
Digital Object Identifier: doi:10.1016/0362-546X(80)90001-2 - C. Cuevas, J.-C. de Souza, S-asymptotically w-periodic solutions of semilinear fractional integro-differential equations, Appl. Math. Lett. 22 (2009), 865-870. Mathematical Reviews (MathSciNet): MR2523596
Digital Object Identifier: doi:10.1016/j.aml.2008.07.013 - C. Cuevas, J.-C. de Souza, Existence of S-asymptotically w-periodic solutions for fractional order functional integro-differential equations with infinite delay, Nonlinear Anal. 72 (2010), 1683-1689. Mathematical Reviews (MathSciNet): MR2577568
- M. Frigon and A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec, 22 (2) (1998), 161-168. Mathematical Reviews (MathSciNet): MR1677243
- A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003. Mathematical Reviews (MathSciNet): MR1987179
- K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.
- H.O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland, Mathematical Studies, 108, North-Holland, Amsterdam, 1985.
- J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41.
- E. Hernández, R. Sakthivel, Rathinasamy and A. Tanaka; Existence results for impulsive evolution differential equations with state-dependent delay, Electron. J. Differential Equations 2008 (2008) no. 28, 1-11.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. Mathematical Reviews (MathSciNet): MR1890104
- Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Unbounded Delay, Springer-Verlag, Berlin, 1991. Mathematical Reviews (MathSciNet): MR1122588
- A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
- C. Lizama, Regularized solutions for abstract Volterra equations, J. Math. Anal. Appl. 243, (2000), 278-292. Mathematical Reviews (MathSciNet): MR1741524
Zentralblatt MATH: 0952.45005
Digital Object Identifier: doi:10.1006/jmaa.1999.6668 - C. Lizama and J. Sánchez, On perturbation of $k$-regularized resolvent families, Taiwan. J. Math., 7, (2003), 217-227.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
- I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999. Mathematical Reviews (MathSciNet): MR1658022
- J. Prüss, Evolutionary Integral Equations and Applications Monographs Math. 87, Bikhäuser Verlag, 1993 Mathematical Reviews (MathSciNet): MR1238939
- R.-N. Wang and D.-H. Chen, On a class of retarded integro-differential equations with nonlocal initial conditions, Comput. Math. Appl. 59 (2010), 3700-3709. Mathematical Reviews (MathSciNet): MR2651845
- K. Yosida, Functional Analysis, 6$^{th}$ edn. Springer-Verlag, Berlin, 1980. Mathematical Reviews (MathSciNet): MR617913
- You have access to this content.
- You have partial access to this content.
- You do not have access to this content.
More like this
- Functional Differential Equations with State-Dependent
Delay on Unbounded Domains in a Banach Space
Benchohra, M. and Hedia, B., Communications in Mathematical Analysis, 2012 - Positive Solutions for System of Nonlinear Fractional Differential Equations in
Two Dimensions with Delay
Babakhani, Azizollah, Abstract and Applied Analysis, 2010 - Stability for a class of fractional partial integro-differential equations
Chuong, Nguyen Minh, Ke, Tran Dinh, and Quan, Nguyen Nhu, Journal of Integral Equations and Applications, 2014
- Functional Differential Equations with State-Dependent
Delay on Unbounded Domains in a Banach Space
Benchohra, M. and Hedia, B., Communications in Mathematical Analysis, 2012 - Positive Solutions for System of Nonlinear Fractional Differential Equations in
Two Dimensions with Delay
Babakhani, Azizollah, Abstract and Applied Analysis, 2010 - Stability for a class of fractional partial integro-differential equations
Chuong, Nguyen Minh, Ke, Tran Dinh, and Quan, Nguyen Nhu, Journal of Integral Equations and Applications, 2014 - The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay
Babakhani, Azizollah, Baleanu, Dumitru, and Agarwal, Ravi P., Abstract and Applied Analysis, 2013 - Existence and Attractivity Results for Some Fractional
Order Partial Integro-differential Equations with Delay
Abbas, S., Benchohra, M., and Diagana, T., African Diaspora Journal of Mathematics, 2013 - Existence of solution of impulsive second order neutral integro- differential equations with state delay
Das, Sanjukta, Pandey, D.N., and Sukavanam, N., Journal of Integral Equations and Applications, 2015 - Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem
Zhang, Xinguang, Mao, Cuiling, Wu, Yonghong, and Su, Hua, Abstract and Applied Analysis, 2013 - Uniqueness and Existence of Solution for a System of Fractional
q
-Difference Equations
Zhou, Wen-Xue and Liu, Hai-zhong, Abstract and Applied Analysis, 2013 - The Solvability and Optimal Controls for Some Fractional Impulsive
Equation
Liu, Xianghu, Liu, Zhenhai, and Han, Jiangfeng, Abstract and Applied Analysis, 2013 - Asymptotic stability of neutral stochastic functional
integro-differential equations with impulses
Diop, Mamadou and Caraballo, Tomàs, Electronic Communications in Probability, 2015


