Stability of Certain Discrete Fractional Equations of Order

Abstract

The equations used to model a real life event is often nonlinear due to the fact that the linear terms fails to bring out various characteristics. Obtaining the exact solution of the nonlinear equation is complicated which makes one to deal with the qualitative properties of the equation. Simple Harmonic Motion (SHM) which is periodic in nature has numerous applications in clock, car shock absorbers, earth quake, heart beat etc and plays a important role in modeling the motion of a particle. In this paper, we consider a initial value discrete fractional equation. The Hyers-Ulam stability and Hyers-Ulam-Mittag-Leffler stability is established for the equation. The stability of discrete fractional simple pendulum equation is established with simulations.