Stepanov Almost Periodic Type Functions and Applications to Abstract Impulsive Volterra Integro-Differential Inclusions

Abstract

In this paper, we analyze various classes of Stepanov-p-almost periodic functions and Stepanov-p-almost automorphic functions (p>0). The class of Stepanov-p-almost periodic (automorphic) functions in norm (p>0) is also introduced and analyzed. Some structural results for the introduced classes of functions are clarified. We also provide several important theoretical examples, useful remarks and some new applications of Stepanov-p-almost periodic type functions to the abstract (impulsive) first-order differential inclusions and the abstract (impulsive) fractional differential inclusions.

Keywords

• Stepanov-<i>p</i>-almost periodic (automorphic) function
• Stepanov-<i>p</i>-almost periodic (automorphic) function in norm
• abstract (impulsive) first-order differential inclusion
• abstract (impulsive) fractional differential inclusion