Maximal Bounds and Approximate Solutions in Quadratic Fractional Integral Equations Involving Mittag-Leffler Q-Type Kernels

Abstract

We establish the existence and construction of maximal solutions for a class of quadratic fractional integral equations (QFIE) whose kernel is a generalized MittagLeffler Q function. Theoretical guarantees are provided under relaxed conditions. The roles of upper and lower solutions are explored, with a monotone iterative scheme yielding maximal bounds. Several concrete examples with specific parameter sets are provided, with graphical illustrations that highlight the typical solution structure. The results are positioned in the context of recent advances in the field