Analysis of fractional derivatives with proportional Caputo Fabrizio and proportional Atangana Baleanu derivatives

Based on the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivatives, we have conducted studies on the Proportional Caputo-Fabrizio and Proportional Atangana-Baleanu fractional derivatives, which constitute a new and original work. New solutions related to the proportional fractional derivative, which can be obtained through Caputo-Fabrizio derivative analysis and Atangana-Baleanu derivatives, have been explored for the fractional derivatives of certain well-known functions. In addition to the analysis of the Proportional Caputo-Fabrizio fractional derivative, the application of the Proportional Atangana-Baleanu derivative to the L-1 transform found in the literature has led to new and original results.