Dynamics of Partial Differential Equations
Volume 8 (2011)
On the new concept of solutions and existence results for impulsive fractional evolution equations
Pages: 345 – 361
In this paper we discuss the existence of PC-mild solutions for Cauchy problems and nonlocal problems for impulsive fractional evolution equations involving Caputo fractional derivative. By utilizing the theory of operators semigroup, probability density functions via impulsive conditions, a new concept on a PC-mild solution for our problem is introduced. Our main techniques based on fractional calculus and fixed point theorems. Some concrete applications to partial differential equations are considered.
impulsive conditions, Caputo fractional derivative, Evolution equa- tions, Cauchy problems, Nonlocal problmes, PC-mild solutions
2010 Mathematics Subject Classification
26A33, 34A12, 34A37, 34G20, 47J35