Convoluted Fractional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>-Semigroups and Fractional Abstract Cauchy Problems
Convoluted Fractional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>-Semigroups and Fractional Abstract Cauchy Problems
We present the notion of convoluted fractional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>-semigroup, which is the generalization of convoluted<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>-semigroup in the Banach space setting. We present two equivalent functional equations associated with convoluted fractional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>-semigroup. Moreover, the well-posedness of the corresponding fractional abstract Cauchy problems is studied.