Analysis of nonlinear integral equations with Erdelyi-Kober fractional operator

作者：Wang, JinRong^*; Dong, XiWang; Zhou, Yong

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(8): 3129-3139.

DOI：10.1016/j.cnsns.2011.12.002

• Nonlinear integral equations
• Erdelyi-Kober fractional operator
• Existence and uniqueness
• Local stability

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.

• 出版日期2012-8
• 单位湘潭大学; 贵州大学