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On a new class of impulsive fractional differential equations

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
242
Identifiers
DOI: 10.1016/j.amc.2014.06.002
Keywords
  • Impulsive
  • Fractional Differential Equations
  • Solutions
  • Stability
Disciplines
  • Mathematics

Abstract

Abstract In this paper, we consider fractional ordinary differential equations with not instantaneous impulses. Firstly, we construct a uniform framework to derive a formula of solutions for impulsive fractional Cauchy problem involving generalization of classical Caputo derivative with the lower bound at zero. In other words, we mean a different solution keeping in each impulses the lower bound at zero, which can better characterize the memory property of fractional derivative. Secondly, we introduce a new concept of generalized Ulam–Hyers–Rassias stability. Then, we choose a fixed point theorem to derive a generalized Ulam–Hyers–Rassias stability result for such new class of impulsive fractional differential equations. Finally, an example is given to illustrate our main results.

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