(<i>F</i>, <i>G</i>, <i>C</i>)-Resolvent Operator Families and Applications

Abstract

In this paper, we introduce and investigate several new classes of (F,G,C)-regularized resolvent operator families subgenerated by multivalued linear operators in locally convex spaces. The known classes of (a,k)-regularized C-resolvent operator-type families are special cases of the classes introduced in this paper. We provide certain applications of (F,G,C)-regularized resolvent operator families and (a,k)-regularized C-resolvent families to abstract fractional differential–difference inclusions and abstract Volterra integro-difference inclusions.

Keywords

• (<i>F</i>, <i>G</i>, <i>C</i>)-resolvent operator families
• abstract fractional differential–difference inclusions
• abstract Volterra integro-difference inclusions
• locally convex spaces
• well-posedness