Existence and controllability of Hilfer fractional neutral differential equations with time delay via sequence method

Abstract

This paper deals with the existence and approximate controllability outcomes for Hilfer fractional neutral evolution equations. To begin, we explore existence outcomes using fractional computations and Banach contraction fixed point theorem. In addition, we illustrate that a neutral system with a time delay exists. Further, we prove the considered fractional time-delay system is approximately controllable using the sequence approach. Finally, an illustration of our main findings is offered.

Keywords

• hilfer fractional derivative
• approximate controllability
• neutral system
• time delay
• mild solutions
• sequence approach
• nonlocal conditions