On a Class of Quadratic Urysohn–Hammerstein Integral Equations of Mixed Type and Initial Value Problem of Fractional Order

2015 ◽  
Vol 13 (5) ◽  
pp. 2691-2707 ◽  
Author(s):  
Mohamed M. A. Metwali
Keyword(s):  
Integral Equations ◽  
Fractional Order ◽  
Initial Value Problem ◽  
Mixed Type ◽  
Initial Value ◽  
Hammerstein Integral Equations ◽  
Equations Of Mixed Type

scholarly journals On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 86-94
Author(s):  
Mohamed M. A. Metwali
Keyword(s):  
Integral Equations ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Orlicz Spaces ◽  
Nonlocal Conditions ◽  
Initial Value ◽  
Hammerstein Integral Equations ◽  
Fixed Point Principle ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractThe existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.

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