Abstract
This paper initiates the investigation of nonlinear integral equations with Erdelyi-Kober fractional operator. Existence and uniqueness results of solutions in a closed ball are obtained by using a directly computational method and Schauder fixed point theorem via a weakly singular integral inequality due to Ma and Pecaric [20]. Meanwhile, three certain solutions sets Y-K,Y-sigma, Y-1,Y-lambda and Y-1,Y-1, which tending to zero at an appropriate rate t (nu), 0 < nu = sigma (or lambda or 1) as t -> +infinity, are constructed and local stability results of solutions are obtained based on these sets respectively under some suitable conditions. Two examples are given to illustrate the results. (C) 2011 Elsevier B.V. All rights reserved.