Volume no :55, Issue no: 1, January (2019)

Journal of Mathematical Sciences: Advances and Applications

HYERS-ULAM STABILITY OF A NONLINEAR MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATION ON BOUNDED TIME INTERVAL

Author's: Huichol Choi, Yongdo Ri, Pak Sun Ae and Kinam Sin
Pages: [21] - [35]
Received Date: January 22, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122029

Abstract

In this paper, we study the Hyers-Ulam stability of a nonlinear multi-term fractional differential equation with Caputo derivative on bounded time interval. First we discuss the existence and uniqueness for the solutions of initial value problem of a nonlinear multi-term fractional differential equation and second we give a criteria for Hyers-Ulam stability which is our main purpose. The technique relies on the fixed point theorem in the Banach space and the equivalence between Chebyshev norm and Bielecki norm.

Keywords

Hyers-Ulam stability, fractional differential equation, Chebyshev norm, Bielecki norm.