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

#### 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.

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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