Impulsive Hilfer fractional differential equations

Abstract

Abstract Existence and controllability results for nonlinear Hilfer fractional differential equations are studied. Sufficient conditions for existence and approximate controllability for Sobolev-type impulsive fractional differential equations are established, where the time fractional derivative is the Hilfer derivative. An example for Sobolev-type Hilfer fractional delay partial differential equation with impulsive condition is considered.

Keywords

• Impulsive condition
• Sobolev-type Hilfer fractional differential equation
• Controllability
• Approximate controllability
• Contraction mapping principle