An existence and uniqueness result for linear fractional impulsive boundary value problems as an application of Lyapunov type inequality


Kayar Z.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.47, ss.287-297, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 47 Konu: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.15672/hjms.2017.463
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.287-297

Özet

A new and different approach to the investigation of the existence and uniqueness of solution of nonhomogenous impulsive boundary value problems involving the Caputo fractional derivative of order a (1 < 2) is brought by using Lyapunov type inequality. To express and to analyze the unique solution, Green's function and its bounds are established, respectively. As far as we know, this approach based on the link between fractional boundary value problems and Lyapunov type inequality, has not been revealed even in the absence of impulse effect. Besides, the novel Lyapunov type inequality generalizes the related ones in the literature.