Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: { ABCaDτθ[x(ϑ)−F(ϑ,x(ϑ))]=G(ϑ,x(ϑ)),ϑ∈J:=[a,b],x(a)=φa∈ℝ.$$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$

The result is based on a Dhage fixed point theorem. Further, an example is provided for the justification of our main result.