Abstract
This paper discusses some existence results for at least one continuous solution for generalized fractional quadratic functional integral equations. Some results on nonlinear functional analysis including Schauder fixed point theorem are applied to establish the existence result for proposed equations. We improve and extend the literature by incorporated some well-known and commonly cited results as special cases in this topic. Further, we prove the existence of maximal and minimal solutions for these equations.
Highlights
In the past few years, many author have utilized the fractional calculus as a path of describing natural phenomena in diverse fields such as mathematics, applied science, and engineering
It is notable that integral equations (IEs) have many useful applications in describing various events and problems of the real world
The existence results will be rely on the following definitions, lemmas and theorems
Summary
In the past few years, many author have utilized the fractional calculus as a path of describing natural phenomena in diverse fields such as mathematics, applied science, and engineering This topic has aroused deep intense interest, and increasing studies of some researchers, both in mathematics and in applications. Our results will be more generalized of the above literature due to the kernel of integration depends on another function ψ, our obtained results will cover a large number of results for different functions of ψ In this regard, we discuss the existence of at least one continuous solution of the nonlinear fractional quadratic functional integral equation t [ψ(t) − ψ(ρ)]α−1 ω(t) = h(t) + g(t, ω(φ(t)). No contributes to study of the fractional quadratic functional integral equations exist in the literature, especially for those involving the ψ-fractional derivatives.
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