scholarly journals Asymptotic behavior of fractional order Riemann-Liouville Volterra-Stieltjes integral equations

2015 ◽  
Vol 27 (3) ◽  
pp. 311-323
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Boualem A. Slimani ◽  
Juan J. Trujillo
Keyword(s):  
Asymptotic Behavior ◽  
Integral Equations ◽  
Fractional Order ◽  
Stieltjes Integral

scholarly journals Singular Lebesgue-Stieltjes integral equations

1941 ◽  
Vol 74 (0) ◽  
pp. 197-310 ◽  
Author(s):  
W. J. Trjitzinsky
Keyword(s):  
Integral Equations ◽  
Stieltjes Integral

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 180
Author(s):  
Oleg Avsyankin
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Integral Equations ◽  
Spherical Harmonics ◽  
Special Class ◽  
Continuous Functions ◽  
Asymptotic Behavior Of Solutions ◽  
Free Term ◽  
Research Technique ◽  
Multidimensional Integral

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

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