Abstract
Using generalized cyclic contractions, we establish some fixed point results in controlled rectangular metric spaces. Some subsequent outcomes are obtained. Moreover, some necessary conditions to demonstrate the existence of solutions for the multi-term fractional delay differential equations with wth order and the piecewise equations under the setting of non-singular type derivative are established in this paper. In order to demonstrate the effectiveness of our results, we provided some numerical examples.
•Karpagam-Zamfirescu type mappings are introduced along with a number of associated fixed point results.•The fixed point method was described and shown, demonstrating how it allows it to apply existence solutions for, nth order multi-term fractional delay differential model and piecewise Caputo-Fabrizio fractional derivative.•Numerical simulations were carried out for various valuesof fractional orders; a system of nonlinear equations was presented and numerically solved.