Abstract
We prove an existence theorem for a nonlinear quadratic integral equation of fractional order, in the Banach space of real functions defined and continuous on a closed interval. This equation contains as a special case numerous integral equation studied by other authors. Finally, we give an example for indicating the natural realizations of our abstract result presented in this paper.
Highlights
Several problems in many branches of science can be modeled as an integral equation such as in physics, engineering, biology,...ect see for example([4], [6], [7], [14])
Quadratic integral equations are applicable in the kinetic theory of gases, in the theory of neutron transport and in the theory of radiative transfer
The most used techniques to study the existence for solutions of an integral equation are based on fixed point argument for example, Banach fixed point theorem was used by many authors in order to establish existence results for different kind of integral equations
Summary
Several problems in many branches of science can be modeled as an integral equation such as in physics, engineering, biology,...ect see for example([4], [6], [7], [14]). Quadratic integral equations have many useful applications in describing problems in the real world. Quadratic integral equations are applicable in the kinetic theory of gases, in the theory of neutron transport and in the theory of radiative transfer. Many existence results for integral equations were established using fixed point theorems involving measure of non-compactness. In this paper we deal with quadratic integral equation of fractional order with respect to another function. Using fixed point theorem via measure of non-compactness Due to Darbo are the main tool in carrying out our proof
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