Hilfer-type fractional differential switched inclusions with noninstantaneous impulsive and nonlocal conditions

Abstract

In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.

Keywords

• Hilfer fractional switched differential inclusions
• noninstantaneous impulsive conditions
• nonlocal conditions
• existence