Impulsive Fractional Dynamic Equation with Non-local Initial Condition on Time Scales
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2207.01517
- arXiv:
- arXiv:2207.01517
- Bibcode:
- 2022arXiv220701517G
- Keywords:
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- Mathematics - Analysis of PDEs;
- 26A33;
- 26E70
- E-Print:
- pp 15