New generalized Ф-Atangana Baleanu Caputo fractional derivative on fuzzy Darboux problem

Abstract

In this study, we initiate a new concept of generalized ?-Caputo Atangana Baleanu fractional derivative by combining the ?-Caputo and Atangana Baleanu fractional derivatives with respect to the generalized Mittag-Leffler kernel which preserves information and solves a variant of Darboux?s Problem for fuzzy implicit fractional differential equations. Using fixed point approach, we prove various existence and uniqueness results. The practical significance of our findings is further proven by an application. The presented results enrich, extend and generalize several prior findings in the literature.