On a fractional integral equation of periodic functions involving Weyl–Riesz operator in Banach algebras

In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involvingWeyl– Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs. © 2007 Elsevier Inc. All rights reserved.