Qualitative review examines the existence and uniqueness of solutions in fractional differential equations, indicating implications for stability in various fields.
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.
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Munzarin A. Sajjan (2026) studied this question.
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