General Fractional Order Quadratic Functional Integral Equations: Existence, Properties of Solutions, and Some of their Applications

Abstract

In this chapter, we are interested in a certain class of integral equations, namely the quadratic integral equation. In this case, the unknown function is treated by some operators, then a pointwise multiplication of such operators is applied. The study of such a kind of problem was begun in the early 60’s due to the mathematical modeling of radiative transfer. The main objective was to present a special method or technique and results concerning various existence for a certain quadratic integral equation.

Keywords: Quadratic integral equation, Carathéodory Theorem, Continuous solution, Iterative scheme, Maximal and minimal solutions, Comparison Theorem, δ -Approximate solutions, Hybrid functional φ-differential equation, Pantograph functional φ - differential equation.

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General Fractional Order Quadratic Functional Integral Equations: Existence, Properties of Solutions, and Some of their Applications

Abstract

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