Integrated Resolving Functions for Equations with Gerasimov–Caputo Derivatives
Vladimir E. Fedorov,
Anton S. Skorynin,
Amar Debbouche
Abstract:The concept of a β-integrated resolving function for a linear equation with a Gerasimov–Caputo fractional derivative is introduced into consideration. A number of properties of such functions are proved, and conditions for the solvability of the Cauchy problem to linear homogeneous and inhomogeneous equations are found in the case of the existence of a β-integrated resolving function. The necessary and sufficient conditions for the existence of such a function in terms of estimates on the resolvent of its gene… Show more
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