Optical applications of a generalized fractional integro-differential equation with periodicity

Impulsive is the affinity to do something without thinking. In this effort, we model a mathematical formula types integro-differential equation (I-DE) to describe this behavior. We investigate periodic boundary value issues in Banach spaces for fractional a class of I-DEs with non -quick impulses. We provide numerous sufficient conditions of the existence of mild outcomes for I-DE utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result. Lastly, we illustrate a set of examples, which is given to demonstrate the investigations key findings. Our findings are generated some recent works in this direction.

Automated summary

In this paper, we propose a mathematical model to describe impulsive behavior using integro-differential equations (I-DE). We investigate the periodic boundary value problems for a class of fractional I-DEs with non-quick impulses in Banach spaces. Utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result, we provide several sufficient conditions for the existence of mild outcomes for I-DE. Finally, we present a set of examples to illustrate the key findings of our research, which are contributed to recent works in this field.