Hadamard fractional discrete-time relaxation equation’s solutions and asymptotic stability

Abstract

This paper suggests two numerical schemes for the famous fractional logistic equations by use of the time scale theory. First, the Hadamard discrete fractional calculus is introduced. Leibniz integral law is used to obtain the fractional sum equation. Then, Hadamard fractional derivative and integral’s numerical schemes are obtained and employed for numerical solutions. It can be concluded the fractional differential equation on time scales is very suitable for both continuous and discrete–time modeling.