Study of Hilfer fractional evolution equations by the properties of controllability and stability

Abstract

This paper is devoted to discuss Hilfer fractional evolution equations through its controllability and stability in a Banach space. We achieve our claims and conclusions by first demonstrating the nature and uniqueness of the suggested set of equations with their mild solutions. The outcomes of existence and uniqueness are obtained with the aid of the propagation family theory, non-compactness calculation methods and the fixed point technique. An example is also provided for the description of our main results.

Keywords

• 26A33
• 34K35
• 47H10
• 47J35
• 93B05
• 93D99