Semilinear fractional order integro-differential equations with infinite delay in Banach spaces

Khalida Aissani and Mouffak Benchohra

Address: Corresponding author: Mouffak Benchohra, Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algérie

E-mail: benchohra@univ-sba.dz

Abstract: This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.

AMSclassification: primary 26A33; secondary 34G20, 34K30, 34K37.

Keywords: semilinear differential equations, Caputo fractional derivative, mild solution, measure of noncompactness, fixed point, semigroup, Banach space.

DOI: 10.5817/AM2013-2-105