Topological Methods in Nonlinear Analysis

Nondecreasing solutions of fractional quadratic integral equations involving Erdélyi-Kober singular kernels

Jie Xin, Chun Zhu, JinRong Wang, and Fulai Chen

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In this paper, we firstly present the existence of nondecreasing solutions of a fractional quadratic integral equations involving Erdélyi-Kober singular kernels for three provided parameters $\alpha \in (1/2\},1)$, $\beta\in (0,1]$ and $\gamma\in [\beta(1-\alpha)-1,\infty)$. Moreover, we prove this restriction on $\alpha$ and $\beta$ can not be improved. Secondly, we obtain the uniqueness and nonuniqueness of the monotonic solutions by utilizing a weakly singular integral inequality and putting $\gamma\in [1/2-\alpha,\infty)$. Finally, two numerical examples are given to illustrate the obtained results.

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Topol. Methods Nonlinear Anal., Volume 44, Number 1 (2014), 73-88.

First available in Project Euclid: 11 April 2016

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Xin, Jie; Zhu, Chun; Wang, JinRong; Chen, Fulai. Nondecreasing solutions of fractional quadratic integral equations involving Erdélyi-Kober singular kernels. Topol. Methods Nonlinear Anal. 44 (2014), no. 1, 73--88.

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