Utpal Kumar Saha | Searcharxiv

arXiv2022

Impulsive Fractional Dynamic Equation with Non-local Initial Condition on Time Scales

In this manuscript we investigate the existence and uniqueness of an impulsive fractional dynamic equation on time scales involving non-local initial condition with help of Caputo nabla derivative. The existency is based on the Scheafer's fixed point theorem along with the Arzela-Ascoli theorem and Banach contraction theorem. The comparison of the Caputo nabla derivative and Riemann-Liouvile nabla derivative of fractional order are also discussed in the context of time scale.

math.AP↗

arXiv2021

Nabla Fractional Derivative and Fractional Integral on Time Scales

In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Grünwald-Letnikov sense. Some of the basic properties and theorems related to nabla fractional calculus are discussed.

math.GM↗