Existence Results of Hybrid Fractional Integro-Differential Equations

Abstract

We study in this paper, the existence results for initial value problems for hybrid fractional integro-differential equations. By using fixed point theorems for the sum of three operators are used for proving the main results.An example is also given to demonstrate the applications of our main results.

Qualitative Study for a Delay Quadratic Functional Integro-Differential Equation of Arbitrary (Fractional) Orders

“…Quadratic integro-differential equations have been discussed in many literature studies, for instance [18,21,22,[24][25][26]. Many real problems have been modelled by Integrodifferential equations and have been studied in different classes.…”

Analysis of Implicit Solutions for a Coupled System of Hybrid Fractional Order Differential Equations with Hybrid Integral Boundary Conditions in Banach Algebras

“…The extensive literature on hybrid differential equations has been thoroughly documented in seminal works by leading scholars. These include significant monographs authored by Ahmad [6], Allaoui et al [7], Awad et al [8][9][10][11], Baleanu [12], Darwish [13], Dhage and Carathéodory [2], Herzallah [14], Krasnoselskii [15], Melliani [16], Zhao [5], and Zheng [17]. These influential publications have played a crucial role in shaping our current understanding of hybrid differential equations, offering profound insights into their nature and behavior.…”

Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra

“…The importance of studying hybrid differential equations lies in dynamic systems include special situations. The consideration of hybrid differential equations is implicit in the work of Krasnoselskii [18] and is extensively covered in many papers on hybrid differential equations with various disturbances, see [4,7,15,16,20,26,27].…”