Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 4

On the new concept of solutions and existence results for impulsive fractional evolution equations

Pages: 345 – 361

DOI: http://dx.doi.org/10.4310/DPDE.2011.v8.n4.a3

Authors

Michal Fečkan (Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Bratislava, Slovakia)

Jin-Rong Wang (Department of Mathematics, Guizhou University, Guiyang, China)

Yong Zhou (Department of Mathematics, Xiangtan University, Xiangtan, Hunan, China)

Abstract

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.

Keywords

impulsive conditions, Caputo fractional derivative, Evolution equa- tions, Cauchy problems, Nonlocal problmes, PC-mild solutions

2010 Mathematics Subject Classification

26A33, 34A12, 34A37, 34G20, 47J35

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