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
Full Text:
FULL TEXTRefbacks
- There are currently no refbacks.