On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function theta. By means of a hybrid fixed point theorem for a product of two operators, an existence result is proved. Furthermore, the sufficient conditions of the continuous dependence on the given parameters are investigated. Finally, a simulative example is given to highlight the acquired outcomes.

Automated summary

This paper discusses a class of hybrid fractional differential equations with fractional proportional derivatives with respect to a continuously differentiable and increasing function theta. An existence result is proved using a hybrid fixed point theorem for a product of two operators. The sufficient conditions for the continuous dependence on the given parameters are also investigated, and a simulative example is provided to demonstrate the acquired outcomes.