A discussion concerning the existence results for the Sobolev-type Hilfer fractional delay integro-differential systems

Abstract

Abstract The goal of this study is to propose the existence results for the Sobolev-type Hilfer fractional integro-differential systems with infinite delay. We intend to implement the outcomes and realities of fractional theory to obtain the main results by Monch’s fixed point technique. Moreover, we show the existence and controllability of the thought about the fractional system with the nonlocal condition. In addition, an application to illustrate the outcomes is also included.

Keywords

• Generalized Caputo fractional derivative
• Hilfer fractional differential equation
• Measures of noncompactness
• Sobolev-type equations