Mild and classical solutions to a fractional singular second order evolution problem
نویسنده
چکیده
Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term. The non-local term is an integral in the form of a convolution of a singular kernel and a regular function involving fractional derivatives. This term may be regarded also as a fractional integral of that regular function. In addition the initial conditions are nonlocal and involve fractional derivatives too. AMS Subject Classification: 26A33, 35L90, 35L70, 35L15, 35L07
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