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

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. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

This paper discusses the controllability and stability of Hilfer fractional evolution equations in a Banach space, demonstrating the nature and uniqueness of the equations and their solutions, and obtaining results of existence and uniqueness through propagation family theory, non-compactness calculation methods, and fixed point technique. An example is provided to illustrate the main results.