Existence of a solution of fractional differential equations using the fixed point technique in extended b-metric spaces

Abstract

The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended b-metric spaces. The considered operators are generalized φ-contractions and α-φ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.

Keywords

• fixed point
• extended b-metric space
• φ-contraction
• α-φ-contraction
• well-posedness
• integral equations
• fractional differential equations