Voir la notice de l'article provenant de la source Library of Science
@article{DMDICO_2013_33_1_a3, author = {Abbas, Sa{\"\i}d and Benchohra, Mouffak}, title = {Existence and attractivity for fractional order integral equations in {Fr\'echet} spaces}, journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization}, pages = {47--63}, publisher = {mathdoc}, volume = {33}, number = {1}, year = {2013}, zbl = {1296.26023}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMDICO_2013_33_1_a3/} }
TY - JOUR AU - Abbas, Saïd AU - Benchohra, Mouffak TI - Existence and attractivity for fractional order integral equations in Fréchet spaces JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2013 SP - 47 EP - 63 VL - 33 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2013_33_1_a3/ LA - en ID - DMDICO_2013_33_1_a3 ER -
%0 Journal Article %A Abbas, Saïd %A Benchohra, Mouffak %T Existence and attractivity for fractional order integral equations in Fréchet spaces %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2013 %P 47-63 %V 33 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2013_33_1_a3/ %G en %F DMDICO_2013_33_1_a3
Abbas, Saïd; Benchohra, Mouffak. Existence and attractivity for fractional order integral equations in Fréchet spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 33 (2013) no. 1, pp. 47-63. http://geodesic.mathdoc.fr/item/DMDICO_2013_33_1_a3/
[1] S. Abbas, D. Baleanu and M. Benchohra, Global attractivity for fractional order delay partial integro-differential equations, Adv. Difference Equ. 2012 (2012), 62. doi: 10.1186/1687-1847-2012-62
[2] S. Abbas and M. Benchohra, Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order, Nonlinear Anal. Forum 17 (2012), 1-9.
[3] S. Abbas and M. Benchohra, On the existence and local asymptotic stability of solutions of fractional order integral equations, Comment. Math. 52 (1) (2012), 91-100.
[4] S. Abbas, M. Benchohra and J.R. Graef, Integro-differential equations of fractional order, Differ. Equ. Dyn. Syst. 20 (2) (2012), 139-148. doi: 10.1007/s12591-012-0110-1
[5] S. Abbas, M. Benchohra and J. Henderson, On global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order, Comm. Appl. Nonlinear Anal. 19 (2012), 79-89.
[6] S. Abbas, M. Benchohra and G.M. N'Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012. doi: 10.1007/978-1-4614-4036-9
[7] S. Abbas, M. Benchohra and A.N. Vityuk, On fractional order derivatives and Darboux problem for implicit differential equations, Fract. Calc. Appl. Anal. 15 (2) (2012), 168-182.
[8] C. Avramescu, Some remarks on a fixed point theorem of Krasnoselskii, Electron. J. Qual. Theory Differ. Equ. 5 (2003), 1-15.
[9] C. Avramescu and C. Vladimirescu, An existence result of asymptotically stable solutions for an integral equation of mixed type, Electron. J. Qual. Theory Differ. Equ. 25 (2005), 1-6.
[10] C. Avramescu and C. Vladimirescu, On the existence of asymptotically stable solutions of certain integral equations, Nonlinear Anal. 66 (2) (2007), 472-483. doi: 10.1016/j.na.2005.11.041
[11] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012.
[12] J. Banaś and B.C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal. 69 (7) (2008), 1945-1952. doi: 10.1016/j.na.2007.07.038
[13] J. Banaś and B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl. 284 (2003), 165-173. doi: 10.1016/S0022-247X(03)00300-7
[14] J. Banaś and T. Zając, Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear Anal. 71 (2009), 5491-5500. doi: 10.1016/j.na.2009.04.037
[15] J. Banaś and T. Zając, A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl. 375 (2011), 375-387. doi: 10.1016/j.jmaa.2010.09.004
[16] M.A. Darwish, J. Henderson, and D. O'Regan, Existence and asymptotic stability of solutions of a perturbed fractional functional integral equations with linear modification of the argument, Bull. Korean Math. Soc. 48 (3) (2011), 539-553. doi: 10.4134/BKMS.2011.48.3.539
[17] B.C. Dhage, Local asymptotic attractivity for nonlinear quadratic functional integral equations, Nonlinear Anal. 70 (2009), 1912-1922. doi: 10.1016/j.na.2008.02.109
[18] B.C. Dhage, Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem, Nonlinear Anal. 70 (2009), 2485-2493. doi: 10.1016/j.na.2008.03.033
[19] B.C. Dhage, Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness, Differ. Equ. Appl. 2 (3) (2010), 299-318.
[20] M. Frigon and A. Granas, Théorèmes d'existence pour des inclusions différentielles sans convexité, C.R. Acad. Sci. Paris, Ser. I 310 (1990), 819-822.
[21] A.A. Kilbas, Hari M. Srivastava and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
[22] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
[23] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
[24] B.G. Pachpatte, On Volterra-Fredholm integral equation in two variables, Demonstratio Math. XL (4) (2007), 839-852.
[25] B.G. Pachpatte, On Fredholm type integral equation in two variables, Differ. Equ. Appl. 1 (2009), 27-39.
[26] I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999.
[27] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
[28] A.N. Vityuk and A.V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil. 7 (3) (2004), 318-325. doi: 10.1007/s11072-005-0015-9