Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel

Abstract

Abstract Using some fixed point theorems for contractive mappings, including α-γ-Geraghty type contraction, α-type F-contraction, and some other contractions in F $\mathcal{F}$ -metric space, this research intends to investigate the existence of solutions for some Atangana–Baleanu fractional differential equations in the Caputo sense.

Keywords

• Atangana–Baleanu derivative in the Caputo sense
• F $\mathcal{F}$ -metric space
• α-type F-contractive mapping
• Atangana–Baleanu fractional operator in the Caputo sense