Existence and asymptotic behavior of non-linear hybrid functional differential equations including the fuzzy Caputo Nabla fractional difference

Aziz El Ghazouani; Fouad Ibrahim Abdou Amir; M'hamed Elomari; Said Melliani

Aziz El Ghazouani Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
Fouad Ibrahim Abdou Amir Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
M'hamed Elomari Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
Said Melliani Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

Abstract

This article considers the fuzzy nonlinear neutral Caputo-Nabla difference equation of order $ 0<\nu <1 $. Krasnoselski's fixed point theorem is used to provide a sufficient condition for the existence of such solutions, and the principle of contraction maps ensures the solution's uniqueness. We provide fascinating results on stability and asymptotic stability. An example has been provided to demonstrate the significance of the results.