Address:
Corresponding author: Mouffak Benchohra, Laboratory of Mathematics, University of Sidi Bel Abbès, PO Box 89, Sidi Bel Abbès 22000, Algeria
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Mohammed Said Souid, Département de Science Economique, Université de Tiaret, Algérie
E-mail:
benchohra@yahoo.com
souimed2008@yahoo.com
Abstract: In this paper we study the existence of integrable solutions for initial value problem for implicit fractional order functional differential equations with infinite delay. Our results are based on Schauder type fixed point theorem and the Banach contraction principle fixed point theorem.
AMSclassification: primary 26A33; secondary 34A08, 34K37.
Keywords: implicit fractional-order differential equation, Caputo fractional derivative, integrable solution, existence fixed point, infinite delay.
DOI: 10.5817/AM2015-2-67