The Solution of Some Nonlinear Integral Functional Equations

الملخص

The integral equation theory is one of mathematical analysis's most important and useful branches. Integral equations occur in a variety of applications, often being obtained from a differential equation, the reason for doing this is that it may make a solution to the problem easier or sometimes, enable us to prove fundamental results on the existence and uniqueness of the solutions. On the other hand, fractional calculus plays an important role in our field of integral equations, and many physical problems can be transformed into integral equations with fractional order. The fractional integral equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bioengineering and others. This paper presents the existence theorems of monotonic solutions for nonlinear functional integral equations by using the Darbo fixed point theorem associated with the Hausdorff measure of noncompactness