Qualitative Analysis of Fractional Differential Equations involving Non-Singular Kernels: A Comprehensive Overview

The existence and uniqueness (E&U) of solutions for fractional differential equations (FDEs) usingnon-singular kernels are thoroughly reviewed in this research study. The Riemann-Liouville and Caputoformulations of traditional fractional calculus rely on singular power-law kernels, which frequently providemathematical difficulties when simulating fading memory processes. To get around these singularities, theCaputo-Fabrizio (CF) and Atangana-Baleanu (AB) operators were recently introduced. In order todemonstrate that solutions to these equations are well-posed, this study examines the fixed-point theorems,particularly Banach and Schauder. We also go over how these operators affect stability analysis and howthey are used in various scientific domains.