Mild and classical solutions to a fractional singular second order evolution problem

作者：Tatar Nasser eddine^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2012, (91): 1-24.

• Cauchy problem
• Cosine family
• Fractional derivative
• Fractional non-local conditions
• Mild solutions
• Second-order abstract problem

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.

• 出版日期2012
• 单位中国石油大学（北京）