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

Jie Xin, Chun Zhu, JinRong Wang, Fulai Chen

Abstract


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.

Keywords


Fractional quadratic integral equations; Erdélyi-Kober singular kernels; nondecreasing solutions; measure of noncompactness

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