Nondecreasing solutions of fractional quadratic integral equations involving Erdélyi-Kober singular kernels
Keywords
Fractional quadratic integral equations, Erdélyi-Kober singular kernels, nondecreasing solutions, measure of noncompactnessAbstract
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.Downloads
Published
2016-04-12
How to Cite
1.
XIN, Jie, ZHU, Chun, WANG, JinRong and CHEN, Fulai. Nondecreasing solutions of fractional quadratic integral equations involving Erdélyi-Kober singular kernels. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 44, no. 1, pp. 73 - 88. [Accessed 14 December 2024].
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