Some novel mathematical results on the existence and uniqueness of generalized Caputo-type initial value problems with delay

Abstract

In this article, we propose some novel results on the existence and uniqueness of generalized Caputo-type initial value problems with delay by using fixed point theory. The characteristics of space of continuous and measurable functions are the main basis of our results. The proposed results are very useful to prove the existence of a unique solution for the various types of fractional-order systems defined under the generalized Caputo fractional derivative consisting of delay terms.

Keywords

• initial value problem
• generalised caputo fractional derivative
• delay
• existence
• uniqueness