Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative

Abstract

Abstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete F $\mathfrak{F}$ -metric spaces for this purpose.

Keywords

• Caputo–Fabrizio fractional derivative
• F $\mathfrak{F}$ -metric space
• α-ℓ-contraction mapping
• Fixed point