Approximate controllability of ?-Caputo fractional differential equation

In this paper, we explain how ?-Caputo fractional differential equations are approximately controllable. The outcome is demonstrated using the infinitesimal operator, fractional calculus, semigroup theory, and Krasnoselskii fixed point theorem. To begin, we emphasize the presence of the mild solution and show that the ?-Caputo fractional system is approximately controllable. Additionally, an example is provided to illustrate the idea.

Automated summary

In this paper, we explain the approximation controllability of ?-Caputo fractional differential equations using the infinitesimal operator, fractional calculus, semigroup theory, and Krasnoselskii fixed point theorem. We emphasize the presence of mild solution and show the approximate controllability of the ?-Caputo fractional system. An example is also provided to illustrate the idea.