| Summary: | In this paper, we introduce and investigate several new classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>F</mi><mo>,</mo><mi>G</mi><mo>,</mo><mi>C</mi><mo>)</mo></mrow></semantics></math></inline-formula>-regularized resolvent operator families subgenerated by multivalued linear operators in locally convex spaces. The known classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-regularized <i>C</i>-resolvent operator-type families are special cases of the classes introduced in this paper. We provide certain applications of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>F</mi><mo>,</mo><mi>G</mi><mo>,</mo><mi>C</mi><mo>)</mo></mrow></semantics></math></inline-formula>-regularized resolvent operator families and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-regularized <i>C</i>-resolvent families to abstract fractional differential–difference inclusions and abstract Volterra integro-difference inclusions.
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