Mixed solutions of monotone iterative technique for hybrid fractional differential equations

TL;DR

This paper develops a monotone iterative method using the Dhage fixed point theorem to find mixed solutions of hybrid fractional differential equations, with applications in biological modeling.

Contribution

It introduces a novel approach combining lower and upper solutions for hybrid fractional differential equations using the Dhage fixed point theorem.

Findings

Established existence of mixed solutions for hybrid fractional differential equations.

Provided an iterative scheme to approximate solutions within bounds.

Applied the method to biological models demonstrating its effectiveness.

Abstract

This paper concerns with a mathematical modelling of biological experiments, and its influence on our lives. Fractional hybrid iterative differential equations are equations that interested in mathematical model of biology. Our technique is based on the Dhage fixed point theorem. This tool describes mixed solutions by monotone iterative technique in the nonlinear analysis. This method is used to combine two solutions: lower and upper. It is shown an approximate result for the hybrid fractional differential equations iterative in the closed assembly formed by the lower and upper solutions.