Author:
Lachachi-Merad Nardjis,Baghli-Bendimerad Selma,Benchohra Mouffak,Karapınar Erdal
Abstract
In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions.
Publisher
Universidad Catolica del Norte - Chile
Reference31 articles.
1. [1] N. Abada, R. P. Agarwal, M. Benchohra and H. Hammouche, "Existence results for nondensely defined impulsive semilinear functional differential equations with state-dependent delay", Asian-European Journal of Mathematics, vol. 1, no. 4, pp. 449-468, 2008. doi: 10.1142/S1793557108000382
2. [2] R. P. Agarwal, S. Baghli and M. Benchohra, "Controllability of solutions on semiinfinite interval for classes of semilinear functional and neutral functional evolution equations with infinite delay", Applied Mathematics and Optimization, vol. 60, no. 2, pp. 253-274, 2009. doi: 10.1007/s00245-009-9073-1
3. [3] N. U. Ahmed, Semigroup theory with applications to systems and control. Pitman Res. Notes Math. Ser., 246. Longman Scientific & Technical. New York: Harlow John Wiley & Sons, Inc., 1991.
4. [4] D. Aoued and S. Baghli-Bendimerad, "Mild solution for perturbed evolution equations with infinite state-dependent delay", Electronic journal of qualitative theory of differential equations, vol. 59, nos. 1-14, 2013.
5. [5] D. Aoued and S. Baghli-Bendimerad, "Controllability of mild solutions for evolution equations with infinite state-dependent delay", European Journal of Pure and Applied Mathematics, vol. 9, no. 4, pp. 383-401, 2016.